//                                               -*- C++ -*-
/**
 *  @brief Sobol' sequence directions
 *
 *  Copyright 2005-2021 Airbus-EDF-IMACS-ONERA-Phimeca
 *
 *  This library is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU Lesser General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This library is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public License
 *  along with this library.  If not, see <http://www.gnu.org/licenses/>.
 *
 * The directions and primitive polynomials are based on the scilab lowdisc module:
 * https://atoms.scilab.org/toolboxes/lowdisc
 * which is covered by the LGPL license
 */

const UnsignedInteger    SobolSequence::MaximumDimension     = 1111;
const UnsignedInteger    SobolSequence::MaximumInitialDegree = 13;

const UnsignedInteger SobolSequence::InitialBase[MaximumDimension * MaximumInitialDegree] =
{
  1,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
  1,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
  1,    1,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
  1,    3,    7,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
  1,    1,    5,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
  1,    3,    1,    1,    0,    0,    0,    0,    0,    0,    0,    0,    0,
  1,    1,    3,    7,    0,    0,    0,    0,    0,    0,    0,    0,    0,
  1,    3,    3,    9,    9,    0,    0,    0,    0,    0,    0,    0,    0,
  1,    3,    7,   13,    3,    0,    0,    0,    0,    0,    0,    0,    0,
  1,    1,    5,   11,   27,    0,    0,    0,    0,    0,    0,    0,    0,
  1,    3,    5,    1,   15,    0,    0,    0,    0,    0,    0,    0,    0,
  1,    1,    7,    3,   29,    0,    0,    0,    0,    0,    0,    0,    0,
  1,    3,    7,    7,   21,    0,    0,    0,    0,    0,    0,    0,    0,
  1,    1,    1,    9,   23,   37,    0,    0,    0,    0,    0,    0,    0,
  1,    3,    3,    5,   19,   33,    0,    0,    0,    0,    0,    0,    0,
  1,    1,    3,   13,   11,    7,    0,    0,    0,    0,    0,    0,    0,
  1,    1,    7,   13,   25,    5,    0,    0,    0,    0,    0,    0,    0,
  1,    3,    5,   11,    7,   11,    0,    0,    0,    0,    0,    0,    0,
  1,    1,    1,    3,   13,   39,    0,    0,    0,    0,    0,    0,    0,
  1,    3,    1,   15,   17,   63,   13,    0,    0,    0,    0,    0,    0,
  1,    1,    5,    5,    1,   59,   33,    0,    0,    0,    0,    0,    0,
  1,    3,    3,    3,   25,   17,  115,    0,    0,    0,    0,    0,    0,
  1,    1,    7,   15,   29,   15,   41,    0,    0,    0,    0,    0,    0,
  1,    3,    1,    7,    3,   23,   79,    0,    0,    0,    0,    0,    0,
  1,    3,    7,    9,   31,   29,   17,    0,    0,    0,    0,    0,    0,
  1,    1,    5,   13,   11,    3,   29,    0,    0,    0,    0,    0,    0,
  1,    1,    1,    9,    5,   21,  119,    0,    0,    0,    0,    0,    0,
  1,    1,    3,    1,   23,   13,   75,    0,    0,    0,    0,    0,    0,
  1,    3,    7,   11,   27,   31,   73,    0,    0,    0,    0,    0,    0,
  1,    1,    7,    7,   19,   25,  105,    0,    0,    0,    0,    0,    0,
  1,    3,    1,    5,   21,    9,    7,    0,    0,    0,    0,    0,    0,
  1,    1,    1,   15,    5,   49,   59,    0,    0,    0,    0,    0,    0,
  1,    3,    1,    1,    1,   33,   65,    0,    0,    0,    0,    0,    0,
  1,    3,    5,   15,   17,   19,   21,    0,    0,    0,    0,    0,    0,
  1,    1,    7,   11,   13,   29,    3,    0,    0,    0,    0,    0,    0,
  1,    3,    7,    5,    7,   11,  113,    0,    0,    0,    0,    0,    0,
  1,    1,    5,   11,   15,   19,   61,    0,    0,    0,    0,    0,    0,
  1,    1,    1,    1,    9,   27,   89,    7,    0,    0,    0,    0,    0,
  1,    1,    3,    7,   31,   15,   45,   23,    0,    0,    0,    0,    0,
  1,    3,    3,    9,   25,   25,  107,   39,    0,    0,    0,    0,    0,
  1,    1,    7,    7,    3,   63,   21,  217,    0,    0,    0,    0,    0,
  1,    3,    5,    7,    5,   55,   71,  141,    0,    0,    0,    0,    0,
  1,    1,    5,    1,   23,   17,   79,   27,    0,    0,    0,    0,    0,
  1,    1,    5,   15,    7,   63,   19,   53,    0,    0,    0,    0,    0,
  1,    1,    3,   15,    3,   49,   71,  181,    0,    0,    0,    0,    0,
  1,    3,    3,   15,   17,   19,   61,  169,    0,    0,    0,    0,    0,
  1,    3,    3,   13,   23,   41,   41,   35,    0,    0,    0,    0,    0,
  1,    1,    1,    3,    3,   59,   57,   15,    0,    0,    0,    0,    0,
  1,    3,    1,    3,    3,    3,  121,  207,    0,    0,    0,    0,    0,
  1,    3,    5,   15,   21,   57,   87,   45,    0,    0,    0,    0,    0,
  1,    1,    1,    5,   25,   33,  119,  247,    0,    0,    0,    0,    0,
  1,    1,    1,    9,   25,   49,   55,  185,    0,    0,    0,    0,    0,
  1,    3,    5,    7,   23,   53,   85,  117,    0,    0,    0,    0,    0,
  1,    3,    3,   13,   11,   57,  121,   41,  235,    0,    0,    0,    0,
  1,    1,    3,    3,   19,   57,  119,   81,  307,    0,    0,    0,    0,
  1,    3,    3,    7,    3,   39,   11,  223,  495,    0,    0,    0,    0,
  1,    3,    3,    5,   11,   21,   23,  151,  417,    0,    0,    0,    0,
  1,    3,    1,   11,   31,    7,   61,   81,   57,    0,    0,    0,    0,
  1,    1,    3,    9,    7,   53,   11,  189,  151,    0,    0,    0,    0,
  1,    3,    7,    1,    9,    9,   35,   61,   19,    0,    0,    0,    0,
  1,    1,    5,    9,    5,   55,   33,   95,  119,    0,    0,    0,    0,
  1,    3,    7,    1,   17,   15,   43,  185,  375,    0,    0,    0,    0,
  1,    1,    3,    5,   23,   59,  107,   23,  451,    0,    0,    0,    0,
  1,    1,    7,    7,   17,   19,  113,   73,   55,    0,    0,    0,    0,
  1,    3,    1,   13,   17,   49,  101,  113,  449,    0,    0,    0,    0,
  1,    3,    3,    9,   25,   31,   29,  239,  501,    0,    0,    0,    0,
  1,    1,    3,    9,   13,    3,   87,   85,   53,    0,    0,    0,    0,
  1,    1,    5,    1,   11,   39,  119,    9,  185,    0,    0,    0,    0,
  1,    1,    1,    7,   31,    5,   97,  201,  317,    0,    0,    0,    0,
  1,    1,    3,    3,   27,    5,   29,   83,   17,    0,    0,    0,    0,
  1,    3,    5,    5,   19,   41,   17,   53,   21,    0,    0,    0,    0,
  1,    1,    5,    1,   17,    9,   89,  183,  487,    0,    0,    0,    0,
  1,    1,    7,   11,   23,   19,    5,  203,   13,    0,    0,    0,    0,
  1,    3,    7,   11,    7,    9,  127,   91,  347,    0,    0,    0,    0,
  1,    1,    7,   13,    5,   57,   89,  149,  393,    0,    0,    0,    0,
  1,    1,    1,    7,   11,   25,  119,  101,   15,    0,    0,    0,    0,
  1,    1,    1,    7,   19,    1,  117,   13,  391,    0,    0,    0,    0,
  1,    3,    3,    9,   19,   15,  103,  111,  307,    0,    0,    0,    0,
  1,    3,    3,    9,    7,   51,  105,  239,  189,    0,    0,    0,    0,
  1,    1,    1,    1,   13,   11,   41,    3,  381,    0,    0,    0,    0,
  1,    3,    1,    1,   21,   19,   83,  205,   71,    0,    0,    0,    0,
  1,    3,    5,    3,   21,   61,   25,  253,  163,    0,    0,    0,    0,
  1,    1,    1,    9,    7,   53,   41,  247,   99,    0,    0,    0,    0,
  1,    3,    5,   15,    9,   29,   55,  121,  467,    0,    0,    0,    0,
  1,    3,    7,    1,   11,   19,   69,  189,  167,    0,    0,    0,    0,
  1,    3,    5,    5,    1,   11,  117,  169,  433,    0,    0,    0,    0,
  1,    1,    1,   13,    5,    9,   49,  179,  337,    0,    0,    0,    0,
  1,    3,    7,    1,   21,   21,  127,  197,  257,    0,    0,    0,    0,
  1,    3,    5,    9,   11,   19,   29,  175,  179,    0,    0,    0,    0,
  1,    3,    3,    9,   13,   43,    1,  217,   47,    0,    0,    0,    0,
  1,    1,    3,    9,   25,   13,   99,  249,  385,    0,    0,    0,    0,
  1,    3,    1,    9,    9,   13,   53,  195,   23,    0,    0,    0,    0,
  1,    3,    5,    9,    7,   41,   83,   95,  117,    0,    0,    0,    0,
  1,    1,    7,   13,    7,   25,   15,   63,  369,    0,    0,    0,    0,
  1,    3,    1,   11,   27,   31,   31,   19,  425,    0,    0,    0,    0,
  1,    3,    7,    3,   15,    9,   73,    7,  207,    0,    0,    0,    0,
  1,    3,    5,    5,   25,   11,  115,    5,  433,    0,    0,    0,    0,
  1,    1,    1,   11,   15,   19,   35,   75,  301,    0,    0,    0,    0,
  1,    3,    7,   11,   21,    5,   21,  217,  147,    0,    0,    0,    0,
  1,    1,    3,   13,   17,   53,   89,  245,  333,    0,    0,    0,    0,
  1,    3,    1,    5,   19,   37,    5,  111,   85,    0,    0,    0,    0,
  1,    1,    7,    3,   19,    7,    1,  189,  221,  519,    0,    0,    0,
  1,    1,    1,   15,   21,   51,   91,  165,  423,  307,    0,    0,    0,
  1,    3,    7,    1,    5,   45,   53,  169,   49,  931,    0,    0,    0,
  1,    3,    3,   11,   11,    7,   35,  141,    3, 1023,    0,    0,    0,
  1,    1,    3,   11,    3,    7,   95,  221,   43,  517,    0,    0,    0,
  1,    3,    5,    7,    5,   61,   83,  249,  229,  771,    0,    0,    0,
  1,    3,    7,   13,   29,   23,   19,  159,  227,  151,    0,    0,    0,
  1,    1,    3,   15,   31,   45,   85,  253,  201, 1023,    0,    0,    0,
  1,    1,    3,   11,   29,    7,   55,  207,  383,  539,    0,    0,    0,
  1,    1,    5,   13,    5,   59,   51,  249,  281,  725,    0,    0,    0,
  1,    3,    1,    9,    5,   41,  101,  219,  229,   45,    0,    0,    0,
  1,    3,    3,   11,    1,    1,   33,   23,  207,  927,    0,    0,    0,
  1,    1,    3,   15,   31,   29,   41,   49,   21,  707,    0,    0,    0,
  1,    3,    1,   15,   27,   61,   55,  127,  343,   29,    0,    0,    0,
  1,    3,    3,   13,   11,   37,   45,  237,  251,  125,    0,    0,    0,
  1,    1,    5,    3,   13,   27,   95,    5,  397,  371,    0,    0,    0,
  1,    3,    1,   15,    1,   47,   61,   25,  173,  275,    0,    0,    0,
  1,    1,    3,    7,    3,   15,   27,  177,  507,  279,    0,    0,    0,
  1,    1,    3,    9,    7,   31,   37,   37,  421,  817,    0,    0,    0,
  1,    3,    3,   11,   11,   35,   89,  103,  443,  389,    0,    0,    0,
  1,    3,    7,   13,    7,   31,   75,   65,  399,  453,    0,    0,    0,
  1,    3,    1,   11,    3,   17,   57,  167,   53,  989,    0,    0,    0,
  1,    1,    1,    9,   23,   51,   61,   81,  345, 1015,    0,    0,    0,
  1,    1,    7,    9,   13,   13,   15,   87,   77,   29,    0,    0,    0,
  1,    1,    3,    5,   31,   25,  117,  119,  385,  169,    0,    0,    0,
  1,    3,    1,   13,   17,   45,   15,   45,  317,  743,    0,    0,    0,
  1,    1,    3,    9,    1,    5,   21,   79,  155,   99,    0,    0,    0,
  1,    1,    7,    1,   27,    5,   27,  143,  187,  923,    0,    0,    0,
  1,    3,    5,   13,   11,   33,   25,   57,  269,  981,    0,    0,    0,
  1,    1,    5,    7,   25,   39,   27,   79,  501,  181,    0,    0,    0,
  1,    1,    7,    7,    1,    5,  123,  187,   19,  693,    0,    0,    0,
  1,    3,    5,    7,   23,   47,   39,  143,  169,  309,    0,    0,    0,
  1,    3,    5,    7,   29,   29,  109,  183,  235,  227,    0,    0,    0,
  1,    1,    3,    7,   17,   35,   93,   75,  415,  111,    0,    0,    0,
  1,    3,    1,    5,   25,   47,   51,   97,   61,  219,    0,    0,    0,
  1,    1,    3,    9,    7,   63,   21,  211,  247,  897,    0,    0,    0,
  1,    3,    3,    7,   25,   45,   91,  149,  183,  377,    0,    0,    0,
  1,    3,    3,   13,   27,   37,  109,  175,    5,  425,    0,    0,    0,
  1,    3,    1,   11,   17,   47,  107,   37,  257,  609,    0,    0,    0,
  1,    3,    3,    9,   13,   59,   45,  135,  401,  227,    0,    0,    0,
  1,    1,    3,   11,   17,   21,   15,  189,  451,   19,    0,    0,    0,
  1,    1,    7,   15,   23,   59,   93,  225,   95,  221,    0,    0,    0,
  1,    1,    3,    3,    5,   33,  127,  241,  455,  143,    0,    0,    0,
  1,    3,    3,   13,   17,   51,    3,   63,   49,  581,    0,    0,    0,
  1,    3,    1,   11,    5,    9,   53,   33,  489,  147,    0,    0,    0,
  1,    1,    7,    1,   13,   27,   81,   43,   75,  919,    0,    0,    0,
  1,    1,    5,   11,   11,   13,   79,   13,  459,  127,    0,    0,    0,
  1,    3,    1,    3,   21,   25,  107,   73,  377,  725,    0,    0,    0,
  1,    1,    7,    3,    5,   43,   79,  213,   87,  793,    0,    0,    0,
  1,    1,    7,    9,   11,    3,   87,   57,  463,  289,    0,    0,    0,
  1,    1,    5,   11,    5,   17,   35,  239,  155,  411,    0,    0,    0,
  1,    1,    7,    1,    9,   21,  109,  183,  233,  835,    0,    0,    0,
  1,    1,    5,    7,   31,   59,   73,  117,  115,  921,    0,    0,    0,
  1,    1,    1,    1,   19,   61,   35,   21,  429,  957,    0,    0,    0,
  1,    3,    3,   15,   17,   27,   83,   29,  211,  443,    0,    0,    0,
  1,    1,    1,   15,    9,   47,  107,  115,  419,  349,    0,    0,    0,
  1,    3,    7,    3,    9,   57,    1,   43,  143,  813,    0,    0,    0,
  1,    1,    3,    1,   27,   11,   51,  205,  487,    5,    0,    0,    0,
  1,    1,    7,    9,   21,   17,    7,  223,  195,  105,    0,    0,    0,
  1,    1,    3,    1,   15,   39,   59,   15,  209,  457,    0,    0,    0,
  1,    3,    5,    7,   15,    1,   33,    3,  461,  393,    7,    0,    0,
  1,    1,    7,   13,    1,   63,  115,  159,  193,  539, 2011,    0,    0,
  1,    3,    3,   11,    1,   21,   43,   51,  157,  101, 1001,    0,    0,
  1,    1,    1,    3,   29,   59,  111,  101,  193,  197,   49,    0,    0,
  1,    3,    3,   13,    5,   17,   45,  127,  363,  697,  825,    0,    0,
  1,    3,    3,   11,   31,   13,  121,   99,  181,   27,  415,    0,    0,
  1,    3,    3,    7,   11,   31,  105,  239,  271,  343, 1441,    0,    0,
  1,    1,    1,    3,   17,    3,  125,  171,  445,  515,  383,    0,    0,
  1,    1,    5,    3,   23,   31,   87,  113,  381,   69, 1581,    0,    0,
  1,    3,    7,    5,   19,    7,  101,  171,  231,  485,  623,    0,    0,
  1,    3,    3,   13,   21,    9,   41,  119,  135,  383, 1621,    0,    0,
  1,    1,    3,   11,   25,   27,   95,  189,  327,  855, 1319,    0,    0,
  1,    3,    7,    5,   15,   37,   75,  245,  403,  693, 1387,    0,    0,
  1,    1,    7,   11,   11,   23,    1,  201,  171,  133,  619,    0,    0,
  1,    3,    7,    1,    5,   31,   57,   27,  197,   87,  839,    0,    0,
  1,    1,    5,    3,    5,    9,  117,  185,  181,  743,  217,    0,    0,
  1,    1,    3,    9,    1,   45,   21,  229,  343,  747,   75,    0,    0,
  1,    3,    1,    7,   19,   43,   27,  105,  113,  475, 1955,    0,    0,
  1,    1,    7,   15,   19,   31,   67,  153,  313,   87,  505,    0,    0,
  1,    3,    1,    7,   19,   63,   29,  189,  393,  469,  281,    0,    0,
  1,    1,    3,    5,    7,   21,   53,   33,  311,  763, 1629,    0,    0,
  1,    3,    7,   13,   13,   39,  117,   35,  415,  721, 1379,    0,    0,
  1,    1,    5,    7,   21,   51,   63,  137,  267,  345,   53,    0,    0,
  1,    3,    3,    9,   17,   27,    1,   77,  247,  479, 1111,    0,    0,
  1,    1,    3,   13,   17,    7,   77,   97,  425,  965, 1399,    0,    0,
  1,    1,    3,   15,   25,   53,   89,   17,  233,  527,  301,    0,    0,
  1,    1,    7,   13,   23,   11,  115,  181,  289,  121,  209,    0,    0,
  1,    3,    1,    9,   19,    1,   49,   55,   55,  271,   49,    0,    0,
  1,    3,    1,    7,   23,   59,  127,  197,   39,  353,  155,    0,    0,
  1,    1,    3,   15,   15,   39,   15,  201,  247,  467, 1647,    0,    0,
  1,    3,    1,    7,   13,   23,   79,  155,  327,  177,  631,    0,    0,
  1,    3,    5,    9,    5,   49,   81,   37,  141,  245,  129,    0,    0,
  1,    1,    7,    5,   19,   23,   29,  197,    5,  627, 1569,    0,    0,
  1,    3,    1,   11,   25,    7,   65,  137,  189,  113,  335,    0,    0,
  1,    1,    3,   11,    9,   55,  103,  223,  183,  357,   67,    0,    0,
  1,    1,    5,   13,    7,   59,   33,   25,   27,    7, 1955,    0,    0,
  1,    1,    3,   13,    3,    3,   73,  179,  337,  691, 1611,    0,    0,
  1,    3,    5,    9,   21,   19,   79,   91,  341,  725, 2021,    0,    0,
  1,    1,    3,    3,   17,   35,   29,   23,  327,  355, 1305,    0,    0,
  1,    3,    3,    5,   25,   13,   21,  235,   87,  889,  121,    0,    0,
  1,    1,    7,   13,    1,    9,  113,   53,  429,  635,   37,    0,    0,
  1,    1,    5,    9,   27,   13,   31,  253,  357,  737,  877,    0,    0,
  1,    3,    5,   11,   25,   15,   33,   49,  265,  429,  835,    0,    0,
  1,    1,    3,   15,   27,   23,  107,  181,  251,  545, 1457,    0,    0,
  1,    1,    3,   11,   25,    9,   95,  249,  437,  925,  669,    0,    0,
  1,    3,    1,    7,    9,    7,  111,   53,  201,  357, 1405,    0,    0,
  1,    3,    3,    1,   13,   43,   59,  173,   29,  873,  935,    0,    0,
  1,    1,    7,    7,    3,   55,   99,   97,  339,  187, 1735,    0,    0,
  1,    1,    7,   13,   17,    3,  117,  247,  257,  351,  665,    0,    0,
  1,    3,    7,    3,   25,   19,   63,   67,  377,  677,  551,    0,    0,
  1,    3,    1,   13,   23,    9,   63,  115,   17,  999,  789,    0,    0,
  1,    3,    5,    3,    9,   27,   99,  103,   53,  921, 1543,    0,    0,
  1,    1,    7,   13,   25,   33,   39,  159,  327,  477, 1267,    0,    0,
  1,    3,    1,    9,    9,   27,    9,  239,   47,  233, 1027,    0,    0,
  1,    3,    3,   15,   13,   49,   35,   69,  375,  765,    1,    0,    0,
  1,    3,    1,    7,   17,   23,   63,  173,  393,  495, 1911,    0,    0,
  1,    1,    1,   13,   17,   47,  125,  217,  369,   81,  163,    0,    0,
  1,    3,    7,   13,    3,   19,   99,   95,  403,  953, 1929,    0,    0,
  1,    1,    1,    3,   15,    7,   45,  221,  125,  479,   67,    0,    0,
  1,    3,    3,   13,    7,   11,   93,  247,  429,   89, 1975,    0,    0,
  1,    1,    1,   15,    7,   55,   33,   97,  257,  173, 1681,    0,    0,
  1,    1,    7,   15,   29,   27,   93,   91,  157,  473, 1413,    0,    0,
  1,    1,    1,   11,    3,   35,    9,  123,  217,  131,  191,    0,    0,
  1,    3,    5,    9,   19,    5,  105,  223,   85,  961, 1711,    0,    0,
  1,    1,    3,   13,   29,    5,   75,  213,  267,  411, 1307,    0,    0,
  1,    1,    5,    9,   29,   55,   51,  129,  117,  291,  401,    0,    0,
  1,    1,    3,   15,   19,   35,  115,  181,  337,  967,  725,    0,    0,
  1,    3,    1,    1,   29,   37,   11,   87,  447,   65, 1229,    0,    0,
  1,    1,    1,    1,   13,    9,   37,  239,  219,  511, 1403,    0,    0,
  1,    1,    5,   15,   15,   33,   17,   85,  501,   13, 1609,    0,    0,
  1,    1,    5,   11,   25,   29,   41,   89,   41,  805, 2035,    0,    0,
  1,    1,    3,   11,   27,   47,   21,  249,   41,  945,  917,    0,    0,
  1,    1,    3,    7,    1,   25,   43,  141,  193,  369,  921,    0,    0,
  1,    3,    5,    1,    3,   11,   73,   39,  509,  827, 1789,    0,    0,
  1,    3,    7,   11,    9,   47,   19,   57,  131,  295,   41,    0,    0,
  1,    3,    1,   13,    9,   53,   93,  249,  207,  163, 2003,    0,    0,
  1,    1,    5,    9,   13,   61,    7,   71,  505,  835,  187,    0,    0,
  1,    1,    3,   13,   31,   59,   95,  101,  421,  259,   67,    0,    0,
  1,    1,    7,    3,   29,    3,   81,  159,  149,  207, 1635,    0,    0,
  1,    1,    7,    5,   31,   53,   93,   33,  111,  331,  717,    0,    0,
  1,    3,    3,   11,    5,   47,   79,  137,  177,   29, 1449,    0,    0,
  1,    3,    5,   13,   15,    5,   81,  189,  167,  315,  277,    0,    0,
  1,    3,    3,    9,   29,   19,   55,   71,  223,  999, 1903,    0,    0,
  1,    1,    3,    9,    1,   59,    9,  253,  291,  133, 1179,    0,    0,
  1,    3,    1,   13,   19,    5,   51,  205,   91,  967,  363,    0,    0,
  1,    3,    7,    1,    5,   47,   63,  171,   29,   41, 1211,    0,    0,
  1,    1,    3,   11,    9,   23,   45,   13,  305,  117, 1231,    0,    0,
  1,    1,    1,   15,   19,   45,   89,  249,  151,  677,  647,    0,    0,
  1,    1,    3,   13,    5,   53,   73,  109,  177,  471, 1261,    0,    0,
  1,    1,    5,    3,   15,    3,   19,  131,  337,  717, 1029,    0,    0,
  1,    3,    7,   13,    3,   49,  115,  199,  183,  881, 1485,    0,    0,
  1,    1,    1,    7,    5,   61,   39,  189,  361,  755, 1309,    0,    0,
  1,    1,    3,   15,    7,   47,   47,  179,  435,  351, 1149,    0,    0,
  1,    3,    7,    1,   15,   39,   81,   31,  307,  723,  317,    0,    0,
  1,    1,    1,   15,   17,   29,   39,   99,  507,  259, 1335,    0,    0,
  1,    3,    5,    3,   17,   17,    5,  113,   77,  879,  171,    0,    0,
  1,    3,    1,    3,   23,   57,    5,   41,  181,  455,  243,    0,    0,
  1,    1,    3,   11,   11,    5,   45,  173,  507,  721,  271,    0,    0,
  1,    1,    1,    7,    9,   17,   53,   23,  315,  289, 1055,    0,    0,
  1,    3,    5,   13,   23,   31,   65,  189,  145,  149, 1601,    0,    0,
  1,    3,    3,    7,   19,   23,   49,  197,  423,  199, 1129,    0,    0,
  1,    1,    1,    7,    3,   41,   17,    3,   71,  805, 1653,    0,    0,
  1,    1,    7,    9,   17,   39,  105,  135,  103,  987,  205,    0,    0,
  1,    1,    1,    7,    1,    5,   13,    9,  493,  851, 1463,    0,    0,
  1,    1,    5,    5,   27,   27,  107,   95,  271,  423, 1681,    0,    0,
  1,    3,    5,   15,    9,    7,    5,  195,  469,  597, 1621,    0,    0,
  1,    1,    5,    9,    9,   29,    5,   27,  339,  129,  197,    0,    0,
  1,    3,    3,    5,   17,   29,   19,  183,  237,   11,  951,    0,    0,
  1,    3,    7,    5,   13,   33,   73,    1,  437,  733,  573,    0,    0,
  1,    1,    1,    7,   25,   31,   59,  123,  483,  549, 1697,    0,    0,
  1,    3,    1,   15,   29,   41,   43,   73,   31,  153, 1265,    0,    0,
  1,    3,    7,   13,   23,   31,   83,   53,  219,  285, 1321,    0,    0,
  1,    1,    3,   15,   29,   29,   97,   99,   61,  451, 1805,    0,    0,
  1,    1,    1,    5,   11,   17,  115,  197,  131,  559, 1235,    0,    0,
  1,    1,    1,   15,   31,   29,   27,   59,  391,  377, 1853,    0,    0,
  1,    3,    7,    5,   25,   29,    1,   27,  233,  109, 1307,    0,    0,
  1,    3,    5,    3,   21,    9,   69,  101,  219,  357,  945,    0,    0,
  1,    3,    7,    1,   29,    9,  103,   55,   69,  143, 1197,    0,    0,
  1,    1,    5,   11,   19,   31,    3,  193,   57,  693, 1411,    0,    0,
  1,    3,    7,    7,   27,   27,   99,   31,  459,  615,  833,    0,    0,
  1,    3,    7,    1,   31,   53,  103,   61,  225,  677,  273,    0,    0,
  1,    1,    3,    5,    3,   35,   63,  119,  421,  701, 1517,    0,    0,
  1,    3,    7,    7,    5,    5,   67,   11,    7,  475, 1747,    0,    0,
  1,    3,    1,    9,    3,   61,   25,    7,  461,  767, 1095,    0,    0,
  1,    1,    3,    3,    3,    1,  121,  255,  111,   85, 1345,    0,    0,
  1,    3,    7,   11,   13,   49,   97,  233,  451,  229,  869,    0,    0,
  1,    1,    7,    1,   21,   13,   77,   53,  277,  509,   57,    0,    0,
  1,    3,    3,   15,    9,   57,   13,  157,  185,  547, 1383,    0,    0,
  1,    3,    5,    1,   29,   29,   83,  193,  193,  151,  221,    0,    0,
  1,    3,    1,    3,    3,    5,  103,   97,  125,  389, 1713,    0,    0,
  1,    1,    1,   15,   17,   21,   41,   83,  251,  711,  335,    0,    0,
  1,    3,    7,   11,   11,   43,   11,   65,  199,  785, 1751,    0,    0,
  1,    1,    1,   13,   11,   25,   27,   81,   73,  657, 1141,    0,    0,
  1,    1,    5,    5,    9,   57,   81,  239,   71,  319,  839,    0,    0,
  1,    3,    5,   13,   21,   49,   37,  167,    7,  509,  523,    0,    0,
  1,    1,    5,    1,   19,   37,   33,   69,  409,   99, 1861,    0,    0,
  1,    3,    1,    7,    7,   27,  125,   71,  417, 1007, 1105,    0,    0,
  1,    1,    5,    1,   17,   11,   71,  109,  149,  775,  389,    0,    0,
  1,    1,    1,   15,   31,   61,   41,   97,  193,  359, 1177,    0,    0,
  1,    1,    7,    7,   25,   37,   41,  137,   53,  697, 1877,    0,    0,
  1,    3,    5,    5,    1,   49,   59,   71,  437,  677,  805,    0,    0,
  1,    3,    5,    1,   27,    5,   41,  193,   29,   85,   93,    0,    0,
  1,    3,    7,    1,    5,   63,   87,  189,  467,  497, 1591,    0,    0,
  1,    1,    1,   15,   15,   63,  123,  115,  229,  105,  423,    0,    0,
  1,    1,    1,   13,   27,    3,   43,   79,   31,  615, 1835,    0,    0,
  1,    3,    7,   11,   29,   45,  101,  205,   35,  891,   99,    0,    0,
  1,    1,    1,   11,   29,   37,   63,   37,   75,   71, 1781,    0,    0,
  1,    3,    7,   13,   29,   63,   45,  227,  105,  449, 1515,    0,    0,
  1,    1,    7,    5,   25,   21,   39,   53,  503,  835, 1909,    0,    0,
  1,    1,    1,   11,   27,   21,   21,   33,   75,  609, 1011,    0,    0,
  1,    1,    1,    7,   25,   19,   97,   91,  317,  377,  303,    0,    0,
  1,    1,    3,    9,    3,   27,   15,  229,  401,  693,  385,    0,    0,
  1,    1,    3,    7,   21,   59,   97,  245,  367,  665, 1635,    0,    0,
  1,    1,    3,    1,   17,   21,  111,  105,  131,  627,  357,    0,    0,
  1,    3,    7,    5,   25,   45,   21,   77,  365,  215,  973,    0,    0,
  1,    1,    7,    3,   13,   23,   49,  229,  441,  911, 1781,    0,    0,
  1,    1,    5,    9,   15,   13,   13,  161,  433,  503, 1707,    0,    0,
  1,    3,    3,    5,   17,   15,   17,  103,   93,  729, 1363,    0,    0,
  1,    1,    7,    5,   13,    3,   79,   93,  377,  131, 1053,    0,    0,
  1,    3,    3,   11,   23,   43,   91,   13,  405,   19,  649,    0,    0,
  1,    3,    1,    5,    9,   63,   65,  161,  465,  895, 1469,    0,    0,
  1,    1,    3,    1,    3,   39,  105,  229,  259,  199,  623,    0,    0,
  1,    1,    7,    7,   11,   19,   75,  223,  283,  161, 1429,    0,    0,
  1,    1,    5,    1,    7,   63,    1,   69,  443,  239, 1241,    0,    0,
  1,    1,    3,   11,    9,   31,   45,   15,  143,  633, 1151,    0,    0,
  1,    3,    3,    7,    9,   41,   67,   25,  445, 1013, 1055,    0,    0,
  1,    1,    5,    9,    7,   41,   83,   23,    3,  537,  503,    0,    0,
  1,    3,    7,   13,   17,   15,  107,  233,  461,  255,  921,    0,    0,
  1,    1,    1,   15,    7,   43,  125,   93,  329,   23,    3,    0,    0,
  1,    3,    1,   13,    1,   63,   87,   25,  309,  149,  349,    0,    0,
  1,    1,    5,    3,   27,   53,   15,  217,   77,  679, 1149,    0,    0,
  1,    1,    5,    1,    1,    1,   81,  247,  323, 1021,  293,    0,    0,
  1,    1,    7,   11,    9,   63,   95,   61,  155,  595,   45,    0,    0,
  1,    1,    7,   13,    5,   31,  105,   75,  347,  199,  303,    0,    0,
  1,    3,    1,   15,   31,    7,   65,   27,   45,  557,  877,    0,    0,
  1,    3,    1,    1,   21,   17,   45,    9,  381,  659, 1565,    0,    0,
  1,    1,    1,    1,   25,   11,   59,  223,  315,  251, 1583, 3915,    0,
  1,    1,    1,   11,   25,   61,  103,  213,  463,  829, 1001,   97,    0,
  1,    1,    5,    9,   21,   31,   23,   55,  207,  727,  663, 3047,    0,
  1,    1,    5,   13,   11,   51,  103,  197,  321,  439, 1535,  937,    0,
  1,    1,    5,    3,    1,   37,   99,  145,  157,  495,  395, 2897,    0,
  1,    3,    7,   13,   23,   29,   67,   89,  109,  647, 1141,  953,    0,
  1,    3,    5,   11,   19,   59,   99,  199,  479,  223, 1481,  127,    0,
  1,    3,    7,   15,   27,   25,   47,   41,  313,  949, 1797, 1201,    0,
  1,    1,    1,   13,   15,   63,  117,  201,  345,  625,  643, 3819,    0,
  1,    1,    1,    9,    3,   59,   71,    5,  167,   87, 1507,  193,    0,
  1,    3,    3,    9,    5,   47,   89,  149,  439,  481,  465, 2053,    0,
  1,    3,    5,    9,   23,   15,   35,   35,  307,   85, 2027, 3061,    0,
  1,    3,    1,    5,    9,   27,   53,  119,  235,  799, 1695, 3759,    0,
  1,    3,    3,    5,   25,   19,   73,  183,  473,  917,  367, 1553,    0,
  1,    3,    3,    5,    7,   29,    9,   53,   79,  769,  937, 2007,    0,
  1,    1,    7,    5,   29,   45,  115,   11,  101,  949,  719, 2493,    0,
  1,    3,    3,    1,   11,   35,   49,   13,  245,  739,  545,  603,    0,
  1,    3,    7,   15,    9,   55,   37,    3,   19,  115, 1991, 3343,    0,
  1,    1,    5,    5,   13,   39,    1,  179,  381,  499,   83, 3751,    0,
  1,    3,    3,    9,    5,   19,   35,  229,  251,  945,  819, 1059,    0,
  1,    3,    5,   11,   11,   43,    9,   43,   35,  547,  239,  783,    0,
  1,    3,    3,    7,    1,   21,   45,   55,   25,  225, 1791, 1789,    0,
  1,    3,    1,   15,    3,   19,   81,  187,  107, 1015, 1461, 1589,    0,
  1,    1,    7,    5,   31,   13,   19,  233,  187,  469, 1647,  283,    0,
  1,    1,    1,    3,   27,   17,  127,   47,  115,  737, 1501, 1093,    0,
  1,    1,    7,   13,    3,   51,   17,  133,  113,  495, 1161, 3919,    0,
  1,    1,    7,    5,   17,   37,   17,   91,  321,  353, 1629, 2747,    0,
  1,    1,    1,    3,   27,    5,  105,   47,  115,  103,  139,  277,    0,
  1,    1,    1,   11,   11,   33,   89,   71,  445,   17, 1595, 2605,    0,
  1,    3,    7,    5,   13,   35,   49,   93,   61,  665, 1921, 2169,    0,
  1,    1,    7,    1,   15,   49,  101,  105,   77,  639, 1267, 2905,    0,
  1,    1,    7,   11,   29,   25,    7,  145,  293,  525, 1415,  721,    0,
  1,    3,    5,   13,   15,   45,   37,   45,  405,   75,  509, 4069,    0,
  1,    1,    5,    9,    1,    1,   33,  255,   13,  447,  347,  233,    0,
  1,    1,    1,   11,   15,   63,   11,  221,   53,  185,  777,  261,    0,
  1,    1,    1,    3,   23,   47,   95,  115,   17,   43, 1083, 1137,    0,
  1,    3,    7,    7,   25,    9,   95,  175,  171,  729,  363, 3993,    0,
  1,    1,    5,   13,   13,   63,   17,   19,  299,  577,  269, 3619,    0,
  1,    1,    5,   15,   21,   15,  111,  129,   41,  863, 1015, 2881,    0,
  1,    1,    7,    1,   15,   25,  105,    5,   79,  735, 1809, 1275,    0,
  1,    3,    5,    7,    3,   25,   41,  209,    3,  317, 1105, 3865,    0,
  1,    3,    1,   11,   29,   15,  115,  197,  485,   99, 1429, 1299,    0,
  1,    3,    1,    1,   29,   41,    5,   57,  331,   17, 1471, 3757,    0,
  1,    1,    5,   13,    5,   13,   69,  177,   13,  477, 2019, 1193,    0,
  1,    3,    5,    1,   25,    3,  101,  115,  257,  893,  381,  733,    0,
  1,    1,    5,   15,   17,   19,   27,  187,   59,  537, 2025,  993,    0,
  1,    1,    5,    1,   11,   51,   27,  119,  201,  519, 1223, 1153,    0,
  1,    3,    5,    9,    7,   49,  101,   77,  497, 1017,  827, 2945,    0,
  1,    3,    5,    7,   15,   37,  103,  211,   81,  375, 1733, 3163,    0,
  1,    3,    1,    3,    5,   25,   53,  111,  451,  297,  887, 3179,    0,
  1,    1,    3,    9,   21,   49,    9,   33,  199,  325, 1321,  437,    0,
  1,    3,    1,   11,    7,   13,   21,  113,  171,  999,  803,  271,    0,
  1,    3,    5,    1,   31,   53,   43,   23,   81,  353, 1951, 3493,    0,
  1,    1,    7,    9,   13,   47,   79,   87,  253,  343, 1297, 3971,    0,
  1,    3,    3,   13,   11,   23,   91,  137,  365,  729, 1995, 1005,    0,
  1,    1,    3,   13,   23,   35,   65,   41,   75,  135,  833, 2615,    0,
  1,    3,    5,    3,    5,   29,  117,    7,  451,  489, 1107, 2253,    0,
  1,    3,    7,   11,    7,   33,   87,   83,  149,  859, 1135, 1131,    0,
  1,    1,    3,    7,   23,   21,  125,   43,  483,  267, 1181,  585,    0,
  1,    3,    7,    9,   27,   35,   55,  121,   81,  141, 1251, 2775,    0,
  1,    3,    1,    1,   21,   23,   45,  145,  453,  831,  983, 2171,    0,
  1,    3,    7,    7,   29,    3,   63,    5,  469,  141, 1389, 2383,    0,
  1,    1,    7,   15,   15,   43,   85,  219,  485,  893, 1565, 2937,    0,
  1,    1,    1,    9,    7,   31,   83,   27,  305,  249,  273, 2447,    0,
  1,    3,    3,    1,   27,   63,   97,   11,  163,  807,  137, 1745,    0,
  1,    3,    5,    5,   27,    9,   45,  111,  401,   53,   71,  663,    0,
  1,    1,    1,   13,   19,    1,   83,  207,   15,  613,  735, 1515,    0,
  1,    3,    5,    5,    7,   61,   87,   55,   91,  131, 1005, 3767,    0,
  1,    1,    5,   11,   15,   43,  113,   97,    3,  547,  933, 2709,    0,
  1,    3,    3,    3,   27,    3,   93,   63,  129,  977,   67, 1767,    0,
  1,    1,    7,    9,   27,   11,   95,  229,   35,  131, 1471, 3185,    0,
  1,    1,    3,   15,   19,   55,    5,   53,  239,  999,  551, 3017,    0,
  1,    1,    7,   11,   19,   11,   17,   33,  355,  175,  457, 2815,    0,
  1,    3,    7,   13,    9,   35,   77,  149,  211,   31, 1667, 1829,    0,
  1,    3,    5,    5,   15,    1,   77,   23,  387,  341, 1729,   87,    0,
  1,    3,    7,    1,    1,   63,  127,  187,  101,  739,  919, 3341,    0,
  1,    3,    5,    7,    3,   35,  123,  153,  299,  467,  285,  793,    0,
  1,    1,    7,    7,   29,   49,   45,   91,   67,  675, 1629, 2627,    0,
  1,    3,    1,    5,   29,   19,   81,  193,  375,  241, 1815, 2169,    0,
  1,    1,    1,   13,    5,   45,   85,  183,  405,  645,  653, 1875,    0,
  1,    1,    5,    7,   27,    9,  121,   59,  357,  247, 1919, 3745,    0,
  1,    3,    3,    7,   31,   57,  119,  211,  267,  391, 1039,  367,    0,
  1,    1,    5,    9,    9,   51,   27,   93,  363,  583,  531, 3783,    0,
  1,    3,    1,    5,    1,    1,   85,  139,   79,  183,  393,  783,    0,
  1,    1,    5,   11,    7,   47,   41,   59,   83,  973, 1411,  827,    0,
  1,    1,    3,   11,    3,   41,   49,  179,  437,  433,  359, 3253,    0,
  1,    1,    7,    1,   19,    9,   15,  163,  457,  367,  221, 2639,    0,
  1,    3,    1,    1,   19,   11,  107,  209,   39,  131,  699, 2955,    0,
  1,    1,    5,   15,   29,   37,   21,   77,   97,  467, 1485, 3539,    0,
  1,    3,    7,    3,    9,   19,   51,   39,  473,  571,  471, 1579,    0,
  1,    1,    7,   13,    3,   55,  119,  111,  289,  309, 1357, 2109,    0,
  1,    3,    3,    9,   21,   23,   11,   79,  179,  385, 1715,  379,    0,
  1,    1,    5,   13,   31,   55,   87,  229,   57,  977,  595, 2939,    0,
  1,    3,    1,    9,   29,   55,  101,   85,   23,  111, 1677, 3019,    0,
  1,    3,    3,    9,   25,   13,  115,  237,   49,  917,  153, 1999,    0,
  1,    3,    5,   11,    1,    7,   63,  199,   79,  935, 1903, 2253,    0,
  1,    3,    1,    5,    3,   47,   63,  137,   71,  473, 1281, 2911,    0,
  1,    3,    5,    5,    9,   37,   37,  147,  341,  345,  215, 3733,    0,
  1,    3,    3,   13,   27,   11,  121,   25,  287,  411,  781,  481,    0,
  1,    3,    3,   15,    5,   43,  109,   73,   95,  313,  543, 1767,    0,
  1,    3,    3,    3,   27,   17,    7,  121,  229,   97,  293, 1055,    0,
  1,    1,    7,    9,   25,    3,   43,  129,  271,  149, 1807, 4019,    0,
  1,    3,    3,   15,   21,   25,   69,   83,  475,  959,  965, 4085,    0,
  1,    3,    5,    3,   11,   19,   19,   87,   49,  841, 1695,  105,    0,
  1,    3,    1,   11,   29,   55,   77,   93,  241,  839,  443, 1829,    0,
  1,    3,    3,   11,   31,   59,   49,  205,  261,  669, 1985, 2097,    0,
  1,    3,    7,   15,   27,   37,   71,  167,  495,  431,  321, 2379,    0,
  1,    1,    7,   15,   21,   33,   59,   53,  353,   51,  879, 1567,    0,
  1,    3,    3,    3,   29,   43,   35,  107,  381,   41, 1227, 2713,    0,
  1,    1,    7,   11,   17,    1,    7,  229,   13,  301, 1915,  737,    0,
  1,    3,    5,   15,    9,    5,   13,  213,  291,  247,  839, 3423,    0,
  1,    3,    3,   15,   17,   21,   55,   95,   37, 1015, 1945, 3941,    0,
  1,    3,    3,    3,   13,    5,  101,  219,  251,  377, 1993, 2659,    0,
  1,    1,    1,    1,   11,   63,  127,  109,  105,  329, 1165, 3961,    0,
  1,    3,    7,    3,   25,   49,  103,  175,  399,  945,   51, 1755,    0,
  1,    1,    5,    1,   15,   61,   85,   13,   81,  269,  557, 3613,    0,
  1,    3,    1,    3,   21,   21,  109,  209,   89,   67,  723, 1937,    0,
  1,    1,    1,    3,   11,   51,   29,   97,  265,  979, 1491, 1559,    0,
  1,    3,    3,    1,   19,   15,   61,   61,  507,  581,  817, 2287,    0,
  1,    3,    7,    3,   31,   19,   67,  147,  205,  643, 1237, 2743,    0,
  1,    1,    1,   13,    3,   43,   21,   19,  145,  823,  947,   67,    0,
  1,    3,    7,    1,   19,   47,  111,   13,  331,  557, 1215, 2859,    0,
  1,    3,    1,   11,    5,   17,   67,  123,  129,   91, 1911,  325,    0,
  1,    3,    7,    5,    3,    9,   23,   73,  119,  405, 1225, 2601,    0,
  1,    3,    3,   15,    3,   53,   57,   35,  503,  117, 1965, 1149,    0,
  1,    3,    7,    7,    9,   45,   75,  141,  249,  801, 1889, 3259,    0,
  1,    3,    3,   15,   13,   11,   71,   81,    1,  509, 1503, 2403,    0,
  1,    3,    5,    9,   13,   51,  101,   19,  289,  347, 1177, 3947,    0,
  1,    3,    7,    1,    3,   25,  123,  171,  463,  893,   73, 2011,    0,
  1,    3,    3,    7,   29,   11,   41,  255,  163,  303, 1767,  175,    0,
  1,    1,    5,    1,    7,   25,  107,  111,  443,  227,  303, 3389,    0,
  1,    1,    3,    9,    5,   47,  101,  107,   63,  783,  177, 3915,    0,
  1,    1,    1,   11,    9,   47,  107,  233,  123,  555, 1897, 1315,    0,
  1,    1,    1,   15,   23,    1,  125,  113,  361,  867, 1401, 2447,    0,
  1,    1,    1,    1,   13,   43,   27,  133,  261,   99,  321,  141,    0,
  1,    1,    5,   13,   21,   29,   47,   89,   49,  703,  921,  359,    0,
  1,    3,    7,    9,   23,   17,  119,    9,  429,  111,  217, 3609,    0,
  1,    3,    7,   13,   21,   31,   41,  231,  137,  797, 1779, 3933,    0,
  1,    1,    3,   11,   31,   15,   19,   95,  355,  873,  327,  729,    0,
  1,    1,    3,    7,   11,   59,  127,   69,  175,  541, 1889, 2051,    0,
  1,    3,    1,    3,    7,   27,   33,   33,  507,  919,  333, 1755,    0,
  1,    3,    1,    7,    7,   63,   31,    1,   59,  513,  615, 2149,    0,
  1,    1,    1,    3,    3,   11,  109,  253,  277,  343, 1665, 2107,    0,
  1,    1,    5,   13,   23,   41,    7,  219,  391,  319, 1825, 1741,    0,
  1,    1,    5,    7,    1,   51,   91,  253,   25,  517, 1639, 1051, 2319,
  1,    3,    7,    9,   23,   29,   91,  247,  185,  135,  237, 3681,  653,
  1,    3,    3,    7,    5,    7,   39,  129,  381,  871, 1205,  471, 1379,
  1,    1,    1,    7,    9,   27,  125,   11,  197,  917,  361, 1055, 1675,
  1,    1,    1,    3,   17,   63,  105,  251,   39,  285,  129,  845, 1951,
  1,    3,    3,    3,   21,   31,   47,  221,    5,  663, 1655,  257, 7075,
  1,    3,    3,    9,    1,   43,  125,  153,  429,  301,  983, 1559, 2087,
  1,    3,    7,    9,   17,    3,  123,   35,  119,   15, 1089, 1061, 7147,
  1,    3,    3,    7,   29,   29,   91,  103,  247,  763, 1171, 2803, 1427,
  1,    1,    3,    5,    7,   39,    9,  239,  177,   89,  401, 2219,  893,
  1,    1,    5,   11,    5,    3,  103,    7,  329,  323,  677, 1315,  171,
  1,    3,    1,   13,   17,   59,   45,   27,  465,  757,  643, 1369, 2019,
  1,    1,    3,   13,   13,   59,   23,  235,  421,  317,  749, 3211, 7235,
  1,    3,    7,    7,   25,    1,  117,  181,  271,  807,  303, 4027, 5697,
  1,    3,    3,    7,   17,   53,    9,    5,  467,  309, 1407,  105, 3615,
  1,    1,    3,   15,    9,   63,  125,  207,  151, 1013, 1873,   11, 1961,
  1,    3,    7,    9,   19,   23,   73,   53,   45,  345, 1579, 1077, 7517,
  1,    3,    3,    5,    9,   63,   11,  149,  429,  499, 1491, 2857, 6849,
  1,    1,    5,    5,    5,   47,   37,  155,  137,  279, 1393,  337, 2893,
  1,    1,    7,    3,    7,   51,   61,  225,  471,  711, 1247, 3553, 1883,
  1,    1,    5,    3,   21,   23,   79,  165,   11,  915,  789, 3503, 2863,
  1,    3,    7,   13,   19,   61,   21,  137,   17,  411,  763, 3917, 2173,
  1,    3,    7,    3,   13,   39,    5,  155,  409,  281,   49, 2665, 4543,
  1,    3,    3,    9,    9,   47,   47,  201,  347,  193,    5, 3823,   73,
  1,    1,    3,    3,    7,   21,  117,   97,  199,  739, 1607, 3403,  381,
  1,    1,    5,    1,    3,   39,   67,  245,  463,  365, 1891, 3711, 3893,
  1,    3,    1,   11,    9,   15,   53,  203,  177,  315,  735, 2085, 6045,
  1,    3,    3,    1,    3,    3,   85,   47,   11,  375, 1557, 1103, 1643,
  1,    3,    5,    3,   15,    9,   33,   39,   51,  809, 1909, 1641, 7669,
  1,    3,    3,   11,   31,   57,   81,   35,  361,  469, 1765,  701, 1027,
  1,    3,    1,   15,   29,   61,  121,  105,   95,  487, 1777, 4095, 1549,
  1,    1,    3,   11,   29,   39,   47,  239,  497,  621, 1127, 2883, 3983,
  1,    1,    5,   11,   25,   37,   61,   49,  163,  857,  813, 1435, 1985,
  1,    1,    1,   11,   13,   21,   51,   15,  351,  975,  695,  653, 6589,
  1,    3,    1,    9,    9,   51,  127,  253,  127,  537,   97, 2363, 7497,
  1,    1,    3,   13,   21,    1,   29,    7,  395,  939,  731, 1597, 2745,
  1,    3,    7,    7,    9,   23,   65,  237,  511,  585, 1503,  767, 2375,
  1,    3,    7,    9,   31,   43,   45,  213,  327,  129, 1751,  869, 7047,
  1,    1,    1,   15,    7,   27,   41,   55,  353,  625,  333, 1825, 1117,
  1,    3,    5,    9,   15,   25,   95,   87,   49,  447,  769, 1117, 1171,
  1,    3,    1,   11,    5,   11,   57,  199,  105,  129,  865, 1297, 1975,
  1,    3,    3,    1,   31,   13,   73,   27,  151, 1017,  693,  501, 5199,
  1,    3,    7,    3,    7,   21,   33,  175,  321,  133,  377,  505, 3915,
  1,    1,    3,    3,   15,   43,  117,   49,  331,   83, 1919,  149, 3695,
  1,    1,    7,    9,   27,    7,   61,   41,  329,    3,  957,  873, 8113,
  1,    3,    3,    7,   25,   11,  111,  229,  509,  415, 1359, 2673, 4303,
  1,    1,    5,   15,   19,   33,   59,   85,  107,  661, 1627,  551, 3773,
  1,    1,    1,   13,    9,   55,  123,    3,  109,   53, 1039, 1499, 7705,
  1,    3,    7,   13,    9,    1,   65,  149,  303,  115, 1783, 2793, 6855,
  1,    1,    1,    7,   25,   37,   47,  179,  467,  903, 1065, 3277, 1675,
  1,    3,    1,   15,   25,   35,  105,  129,  287,   49, 1665, 2143, 2245,
  1,    1,    3,    9,   23,   27,   23,  185,  161,   79, 1917, 3663, 2817,
  1,    3,    5,   13,    1,   61,   29,  249,   45,   55, 1947,  533, 1719,
  1,    1,    3,    9,    9,   39,  107,  197,  385,  385,  991, 3991,  569,
  1,    3,    7,   15,    7,    5,   37,   15,  289,  261, 1997,  575, 1021,
  1,    3,    1,   13,   11,   19,   81,   97,  363,  345,  841, 1877, 2077,
  1,    1,    5,   15,   15,   61,   67,  197,  331,  297,  459, 1009, 5945,
  1,    1,    5,    9,   19,   61,   29,  139,  265,  199,  221, 3929, 1833,
  1,    3,    1,   13,   15,   57,  115,  203,  407,  385,  327,  473, 2631,
  1,    3,    1,    1,   27,   59,  119,   63,   37,  617, 1595, 3009, 4851,
  1,    1,    3,   11,   17,   21,   75,   33,  433,   25, 1881, 2595, 6371,
  1,    3,    1,    7,   11,   59,   73,  251,  315,  515, 1269, 3249,  833,
  1,    3,    3,   11,   11,   61,   99,  217,  343,  275, 1007,  675, 7987,
  1,    1,    3,    3,   31,   57,  103,  199,   63,  849,  129, 3593,  331,
  1,    3,    7,   13,   13,   25,    7,  199,   51,  401, 1413, 2453, 1899,
  1,    3,    1,    5,   25,   55,   57,   99,  185,  471,  475, 1567, 8093,
  1,    1,    7,    1,   25,   27,   45,  249,   71,  377, 1105,  973, 6719,
  1,    1,    3,    7,    9,   31,   61,   33,   27,  661,  791,  595, 6903,
  1,    3,    1,   15,    7,   41,   95,  229,  267,  535, 1983, 1335, 5903,
  1,    1,    7,    3,   13,   33,   49,  177,  503,  505, 1359, 1715, 5657,
  1,    3,    3,   13,   29,   63,  101,   13,  239,  939,  503,  589, 5007,
  1,    3,    1,    7,   19,   19,  101,  209,  293,  465,  691,   85, 2689,
  1,    1,    7,   13,    5,   57,   35,  147,  245,  225,  659, 2265, 6637,
  1,    1,    3,   13,   19,   35,   47,   97,  281,  929,  691, 3069, 2675,
  1,    3,    5,   11,   31,   13,  119,   31,  297,  219,  343,  461, 1645,
  1,    1,    3,    3,   25,   63,   39,  125,   75,  955, 1375, 1659, 1819,
  1,    3,    5,    5,   13,   35,   67,  177,  461,  659, 1919, 2627,  689,
  1,    1,    7,    3,   25,   17,   31,  137,  371,  441,  263, 1307, 6709,
  1,    3,    3,   13,   15,   11,  103,  187,  129,  117, 1373, 1731, 7717,
  1,    1,    3,   11,    5,   11,    7,   11,  189,  527,  603, 1501, 6295,
  1,    1,    3,    9,    9,   49,   61,   91,  189,  427, 1383, 1699, 7013,
  1,    3,    5,    9,   29,   41,  127,  223,  339,  515,  297, 3545, 7695,
  1,    3,    1,    3,   31,   55,   87,   29,  287,  287,  781, 3803, 3705,
  1,    1,    7,   11,    9,    5,    3,  169,  111,  191,  145, 2157, 7069,
  1,    1,    7,   11,   29,   45,   35,  231,  111,   33,  285,  453, 2621,
  1,    1,    1,    7,   27,   17,   29,   59,  379,  389,  767, 2813, 3631,
  1,    3,    3,    9,   25,   35,   73,   31,   93,  197, 1739, 2047, 6571,
  1,    3,    1,   13,   27,    5,   95,  163,   27,  825, 1715, 2999, 6259,
  1,    1,    3,   11,   11,   31,  103,   41,  185,   63,  715, 3841, 7261,
  1,    3,    7,    7,   17,   31,   71,   57,  347,  417,  317, 2361, 3397,
  1,    1,    7,   15,    5,   37,   75,   87,  337,  949, 1333, 1079, 7645,
  1,    1,    1,   13,   17,   17,   51,  247,  247,   35,   85,  573, 1115,
  1,    3,    3,    7,    3,   45,   87,   25,  507,  571,  831,   69, 4753,
  1,    3,    7,    5,   23,   51,   57,  127,  161,    9, 1615, 1363, 2047,
  1,    1,    3,    3,   15,    1,   97,  101,  231,  131,   81, 1597, 7579,
  1,    1,    1,    1,    9,   39,   11,  207,   43,  609, 1667, 3427, 2271,
  1,    3,    5,    5,    9,   49,  105,  187,  499,  439, 1467, 2899, 5403,
  1,    1,    3,   15,   17,   55,   87,   73,   73,   95, 1457, 2771, 4911,
  1,    3,    1,   15,   17,   19,   41,   61,  327,   19, 1453, 1327, 7629,
  1,    1,    1,    3,   31,   41,   73,  105,  263,  569, 1825, 1117, 4225,
  1,    1,    1,   11,   11,   13,  109,   27,  331,  893,  109, 1523, 1209,
  1,    1,    5,    1,   19,    5,   69,   91,  249,  451,  387, 3521, 6955,
  1,    1,    3,    7,   25,   51,   35,  171,  493,  397, 1207, 2393, 6951,
  1,    1,    3,    3,   13,    5,  121,  243,   37,  971, 2039, 2537, 1829,
  1,    3,    7,   15,   23,   49,   39,   33,   25,  801,  213, 1979, 5579,
  1,    1,    1,   11,   15,    1,  111,    3,  115,  125, 1351, 3179, 5231,
  1,    1,    5,    5,   25,   21,    1,    1,    3,  471, 1329,  683, 1783,
  1,    1,    3,    5,   21,   13,   77,   21,  167,  187, 1173, 2453, 4285,
  1,    1,    5,    3,   31,   17,   39,  229,  197,  257,   57,  453, 7425,
  1,    3,    1,    5,   19,   59,   47,   93,  127,   67, 1769, 1227,  599,
  1,    1,    3,    5,    3,   51,   53,   71,  357,  949,  951,  779, 5785,
  1,    3,    1,    1,   11,   11,   91,   61,  497,  621,  183,  671, 3275,
  1,    1,    3,   15,   25,    3,    3,   37,  103,  453,   23, 3483, 5643,
  1,    1,    1,    5,    7,   61,   17,  183,  125,  411,  451, 2135, 2263,
  1,    3,    5,    1,   15,    1,   51,   65,  191,  621, 1155, 3139,  657,
  1,    3,    7,    5,   19,   33,   83,  211,  165,  955, 1551, 3381, 6769,
  1,    1,    7,    3,    7,   37,   39,   53,   55,  309, 2037, 3945, 6261,
  1,    1,    1,    7,    5,   33,  125,   11,  101,  783,  811,   57, 1251,
  1,    3,    1,    5,    3,   61,   85,  151,   95,  893,  635, 1541, 3249,
  1,    1,    5,   11,   13,   25,  111,  165,   79,  597, 1671, 3405, 4447,
  1,    3,    3,    3,   13,   27,   21,   47,  351,  377, 1451, 3381, 4111,
  1,    1,    1,   13,    1,   59,   69,    5,  341,  753,  863, 2371, 3991,
  1,    3,    5,    9,   23,    7,   85,  129,   43,  145, 1499, 2879, 1215,
  1,    3,    1,   13,    5,   49,   29,   79,  125,  637, 1673, 1985,  131,
  1,    3,    1,   15,   25,   13,   55,  101,  135,  941,  363,  987, 4397,
  1,    1,    7,    5,   11,   63,   11,  147,  173,  593, 1029, 3017, 3487,
  1,    3,    7,    3,   25,    3,  117,  169,  289,  317, 1077, 3031, 7585,
  1,    3,    3,    5,   15,   33,    1,  181,  373,  555, 1525, 3839, 5565,
  1,    3,    5,    9,   13,    3,   47,   19,  133,  375,  277, 1401, 7199,
  1,    1,    5,    5,   21,   15,   17,   95,  421,  575, 1023, 3749, 3573,
  1,    1,    1,    3,   11,    9,   65,   77,  241,  175,  655, 2977, 7105,
  1,    3,    7,   11,   23,   13,   63,  139,  281,  403,  665,  681, 7409,
  1,    3,    1,    1,   29,   35,   47,  197,  213,  571, 1869, 1175, 1671,
  1,    3,    5,   13,    5,   39,  117,  219,  177,  555, 1255, 1519,  949,
  1,    1,    1,    9,   17,   11,   17,   97,  363,  109,  965, 3355, 3889,
  1,    1,    1,   15,   27,   59,  115,  239,  151,  377,  277,  907, 5971,
  1,    1,    3,    3,    9,   59,   51,  183,  227,  931, 1601,  117, 3333,
  1,    1,    1,    5,   19,    1,   25,  143,  145,  499,  329,  771,  225,
  1,    3,    5,   11,   15,   57,   33,    9,  363,  649, 1603, 3741, 3647,
  1,    1,    7,    9,    5,   11,  123,   13,  239,  653, 1901, 3337, 5403,
  1,    3,    5,    1,   29,    5,  123,  209,  431,  329,  395, 1743, 3409,
  1,    1,    7,    3,   23,   57,   83,   23,   81,  279,   65, 1227, 7459,
  1,    3,    7,   15,   19,   13,   51,  215,  397,  271, 1307, 3335, 6879,
  1,    1,    1,    9,    1,   31,  113,   53,  241,  647, 2029, 2755, 5789,
  1,    1,    5,    9,   27,   13,   95,  137,   67,  721,   21, 1909, 6567,
  1,    3,    1,    9,    3,   11,  121,  203,  291,  665, 1321, 3603, 5581,
  1,    3,    1,   11,   23,   55,   51,   19,  255,  429,  543, 2397, 4919,
  1,    1,    3,    7,   21,   45,   91,  151,  405,  957, 1569,  653, 1927,
  1,    1,    5,    5,   19,    9,  109,  171,  421,  803, 1185,   87, 4407,
  1,    1,    1,   13,   27,   55,   43,  133,  399,  767, 1905, 2025, 8085,
  1,    3,    5,    1,   11,   55,   55,  219,   75,  425, 1701, 2617, 4691,
  1,    3,    5,   15,   17,   19,   35,  231,  399,  477,  413, 3257,  611,
  1,    1,    3,    3,   13,   25,   55,    3,  105,  995, 2041,  287, 3005,
  1,    3,    1,   13,   27,   41,   87,   15,  329,  105, 1697, 3051,  591,
  1,    1,    3,    9,   11,   23,   33,  253,   41,  495,  725, 3809,  753,
  1,    3,    1,   13,   31,   45,   37,  225,  425,  575, 1417,  897,  589,
  1,    1,    5,    5,   23,   29,    5,   33,    7,  687, 1847, 2215,  171,
  1,    1,    5,    1,    5,   63,    3,  111,  283,  385,  411,   63, 5729,
  1,    1,    3,    5,    9,   59,   45,  183,  375,  227,  211, 2043, 5891,
  1,    1,    3,    1,   21,   27,   21,  213,  475,  923,  915, 1757, 1033,
  1,    1,    3,   13,   31,   39,  105,  169,  427,  563, 1891, 3671, 3049,
  1,    1,    3,   13,   29,   21,  127,  119,  277,  723,   17,  297, 6567,
  1,    3,    1,    7,   11,   37,   35,  111,  209,  481, 1877, 3131, 5257,
  1,    1,    1,    7,   21,    7,   17,   15,  411,  717, 1699, 1305, 8003,
  1,    3,    3,    1,   17,   61,   35,  201,    3,  111,  687,  293, 1757,
  1,    3,    1,    9,   15,   49,   37,  123,  137,  633, 1089, 3865, 4489,
  1,    1,    3,    5,    7,   35,   97,  121,  195,  113, 1973, 3173, 4923,
  1,    3,    5,   11,   15,   39,   97,  225,  289,  369, 1809, 3397, 6379,
  1,    3,    5,    9,    7,    9,   21,  113,  509,  955,  851, 2269, 5171,
  1,    3,    7,   11,    9,   29,   77,  113,  121,  253, 1495, 3673, 1757,
  1,    1,    5,   13,   21,    7,  123,  225,   55,  321, 1257,  717,  689,
  1,    3,    5,    3,   27,   25,   17,  161,  147,  409,   63, 3041, 3081,
  1,    1,    7,   15,   25,   23,   89,  165,  275,  909, 1323, 3341, 1389,
  1,    1,    5,   15,   29,   57,   53,    1,  251,  367, 1307, 3595, 4113,
  1,    3,    7,   13,   11,    5,  105,  139,   19,   33,  609, 3819,  455,
  1,    3,    1,   15,    3,   19,   75,   55,  129,  967,  881, 2871, 2761,
  1,    1,    3,    7,   21,   15,   25,    3,  285,  453, 1543, 3973,  847,
  1,    1,    7,    5,   13,   33,  125,   93,  415,  863,  177, 1129, 7575,
  1,    3,    7,    7,   23,   49,   13,  217,  487,  449,  617,  513, 5829,
  1,    3,    3,    9,   19,   37,   47,  193,  491,  539, 1505,  871,  633,
  1,    1,    5,    7,   27,   25,   21,   97,  193,  781, 1747, 1485, 6629,
  1,    1,    5,    9,   17,   17,  125,   29,  219,  911, 1537, 3977, 1103,
  1,    1,    7,    9,   29,   45,   23,   69,  403,  113,  925, 2473, 7635,
  1,    3,    5,    9,   25,   29,   55,  231,   23,    7,  183, 1171,  803,
  1,    1,    5,   11,   17,   15,   63,  161,   97,  219,   77, 1143, 6175,
  1,    3,    3,    9,    9,   25,   61,   93,   65,  725, 1723, 3063, 6587,
  1,    3,    3,    3,    1,    3,    5,   69,  285, 1015, 1877, 3547, 2711,
  1,    1,    3,   11,   19,    3,   17,  143,   75,  971, 1703, 2183, 3879,
  1,    1,    1,   15,   23,   49,   93,  137,   21, 1021,  397, 3993,   67,
  1,    3,    7,   13,    5,   11,   57,    9,  373,  525,  459,  133, 1179,
  1,    1,    1,   13,   23,   39,  121,   87,  261,  785,  521, 2529, 4761,
  1,    1,    5,    5,    1,   15,   69,  183,  339,  873,  257, 2699, 7281,
  1,    3,    5,    9,   17,   19,   73,  113,  239,  191, 1177,  233, 1557,
  1,    1,    5,   15,   17,   57,   93,  183,  495,  893,  389, 2355, 3379,
  1,    3,    3,    1,   13,   39,  121,   73,  415,  297, 1947,  231, 2459,
  1,    1,    3,    1,   27,   15,  105,  215,  333,  507, 1553, 3241, 4273,
  1,    1,    5,    9,   23,   11,   75,  137,  107,  215, 1583,  611, 4127,
  1,    1,    1,    5,    7,    3,   91,   89,  435,   21, 1831, 1309, 7147,
  1,    3,    3,   13,    7,   57,   67,  251,  297,  153,  261, 3829,   35,
  1,    3,    1,    3,   11,   31,   95,  163,  213,  645,  485, 1839, 3549,
  1,    3,    3,   13,   13,   55,   75,   41,  149,  913,  289, 1495,  395,
  1,    3,    3,   15,   17,   61,    9,  227,  463,  755, 1281,  301, 3735,
  1,    1,    3,    3,   13,   19,   69,  145,  199,  371, 1543, 1169, 5787,
  1,    1,    7,    1,   11,    5,   97,   57,  323,  881, 1591, 1613, 4179,
  1,    3,    1,    3,   21,   41,   99,   81,   45,  113, 1123, 2673, 5889,
  1,    3,    7,   11,   13,   35,   93,   57,   19,  903,  573,  243, 5057,
  1,    1,    7,   13,   23,   59,   11,   11,  301,  225,  821, 3601, 7473,
  1,    1,    3,    1,    1,   61,   53,  135,  121,   49, 1065, 3669, 4713,
  1,    1,    7,   15,   27,   39,   19,  145,  499,  587, 1933, 2813, 2133,
  1,    1,    1,    9,   13,   41,   73,  161,  187,  201, 1373, 2671, 2897,
  1,    3,    1,    9,    9,   53,    5,  175,  229,  927, 2005, 2679, 1841,
  1,    1,    5,    3,    7,   53,   33,  159,   63,  429,  905, 3463, 2125,
  1,    1,    7,    1,    1,   63,   79,   25,  425,  599,  207, 2477, 1029,
  1,    3,    1,    9,   27,   31,  107,   55,   99,  513,  173, 1795, 1695,
  1,    3,    7,    1,   29,    9,   65,  167,  281,   97, 1573,  617, 6523,
  1,    3,    1,    9,    5,   59,   69,  157,   35,  319, 1597, 2317, 1143,
  1,    1,    7,    1,   13,   13,   79,  211,  125,  331,  573, 1855, 5105,
  1,    1,    7,   13,   25,   35,  125,   97,  349,  833, 1883, 1057, 7133,
  1,    3,    1,   11,   21,   55,   25,  247,   87,  325, 1795, 1703, 3351,
  1,    3,    3,   15,    3,   41,   93,  249,  101,  887, 1499, 1761, 2775,
  1,    1,    7,    7,   31,   49,   55,   23,   59,  139, 1743, 2515, 3971,
  1,    3,    5,   11,   15,    5,   61,  129,  195,  927,  553,  801, 4503,
  1,    3,    1,   15,   13,   41,   17,  159,  511,  399,  335, 1205, 7589,
  1,    1,    3,   13,    3,   25,  117,   71,  355,  163,  333, 1311, 5155,
  1,    1,    5,   15,   19,   27,   69,  197,   73,  307, 1645,  473, 4305,
  1,    3,    5,    1,   13,   43,   97,  127,  263,  803,  791, 3963, 1641,
  1,    3,    5,    9,    1,    5,   87,  141,  243,  169,  871,  697, 4717,
  1,    3,    1,    9,   27,    5,  111,  219,  101, 1019, 1157, 1221, 2427,
  1,    3,    1,    7,   15,   43,   37,    5,  165,  869,  969,  251, 5617,
  1,    3,    7,    3,   17,    5,   93,  233,  141,  537,  557,  381, 1267,
  1,    3,    1,    5,    1,    5,   59,  131,   11,  907,  141, 3887,  399,
  1,    3,    7,   11,    3,   17,   79,  217,  389,  479,  223, 1761, 5831,
  1,    1,    1,    7,   13,    5,   95,  101,  219,  335, 1129, 3093, 4305,
  1,    3,    7,    3,   13,   15,   53,  131,  187,  697, 1685, 3721, 4241,
  1,    3,    7,    9,   13,   27,  115,   33,  449,  479,  423, 2079, 3395,
  1,    1,    3,    5,   31,   29,   53,  157,  447,  353, 1069, 4085, 3045,
  1,    3,    1,   15,   29,   17,   85,  173,  393,  769,  391,  379, 4899,
  1,    1,    1,    7,   27,    9,   85,   69,  477,  787,   99, 3601, 1713,
  1,    3,    5,    5,    7,    3,   65,  207,  305, 1023,   95, 3845,  171,
  1,    1,    1,    3,    7,   55,   59,  239,  221,  855, 1847,  433,  411,
  1,    1,    5,   13,   21,   31,   23,   81,   51,  493,  531, 1781, 7099,
  1,    3,    1,    7,   29,    1,   75,  205,  355,  883, 1859,   29, 5473,
  1,    3,    5,    1,   15,   45,   21,   11,  209,  521, 1833, 1897, 5209,
  1,    1,    3,    1,   17,   45,   67,   41,  499,  735, 1833, 1599, 1195,
  1,    1,    5,    9,   17,   13,   27,  169,  479,  297,  341, 2163, 1077,
  1,    1,    5,   15,   21,   57,   99,   65,  265, 1011,  237,   75, 1309,
  1,    3,    5,   15,   19,   17,   79,  193,  377,  991, 1997, 3475, 2953,
  1,    1,    5,   15,   17,    3,   27,   77,  145,  879, 1799, 3957, 7343,
  1,    3,    5,   11,    3,   61,    3,  201,  411,  855,  409, 1641, 4887,
  1,    3,    3,    3,   15,   15,   95,  173,  173,  591,  431, 3911, 3229,
  1,    1,    3,    5,    5,   49,   27,    1,   11,  415, 1917, 2959, 6759,
  1,    3,    7,   15,   27,   15,   69,  221,  433,  917,  363, 2833, 6721,
  1,    3,    3,   13,   27,   47,   19,  157,  483,  375,  335, 1279, 6775,
  1,    1,    3,    7,    3,    9,   75,    1,  135,  453, 1039, 1099,  675,
  1,    3,    5,   15,   31,   37,   47,   15,  385,  553, 1085,  403, 4039,
  1,    1,    5,   15,   31,   45,   59,  113,  341,  189, 1657,  799, 2493,
  1,    1,    3,   11,    7,    9,   41,  147,   89,  841, 1975, 2183, 7511,
  1,    3,    7,   11,   21,   51,   85,  137,  209,  339, 1527, 2699, 3269,
  1,    3,    1,    9,    3,   61,   77,  205,  391,  211, 1111, 1711, 4199,
  1,    3,    5,    5,   13,   21,   99,  225,   33,  601,  659, 2037, 6625,
  1,    1,    7,   15,   11,   33,   55,   73,  395,   57,  389,  727, 7943,
  1,    1,    5,    9,   17,   11,   49,   45,  319,  765,  899,  289, 2013,
  1,    1,    1,    7,   27,   21,   93,   49,  451,  745,  595, 1785, 4145,
  1,    3,    5,    3,   25,   63,   93,  149,  119,  621, 1439, 1575,  667,
  1,    1,    5,   13,    1,   63,  119,  113,  341,  209, 1861, 3633,  513,
  1,    1,    3,    1,    9,   47,   51,  253,  227,  875, 1979, 2367, 2303,
  1,    1,    5,    1,    7,   57,  125,   99,  375,  639, 1569, 1261, 4591,
  1,    3,    5,    5,   29,   61,   63,   17,   61,    7, 1087, 3953, 7941,
  1,    3,    7,    1,   27,   49,   13,  119,  331,  595, 1009, 1735, 2741,
  1,    3,    5,    3,   21,    9,   15,  105,  493,  971,  165,  171,  987,
  1,    1,    3,    1,   23,   59,   45,  117,  411,  263, 1895, 1959, 8061,
  1,    3,    5,    7,   13,   19,   61,  129,  293, 1009, 1481, 2867, 3161,
  1,    3,    5,    1,   25,   29,   19,  243,   47,  201, 1583,  859, 5951,
  1,    1,    5,    1,   29,   21,  105,   75,  203,   23,   29, 2951, 1431,
  1,    3,    1,    5,   15,   23,  115,  203,  375,   77, 1193, 3211,  831,
  1,    1,    5,    1,   17,   55,   17,   53,  167,  621, 1673,   15, 5559,
  1,    1,    5,   11,   29,   23,   83,   29,  395,   33, 1075, 1279, 7405,
  1,    3,    5,   11,    9,   43,    7,  247,  155,  535,  301, 1323, 1357,
  1,    3,    5,    9,   15,   41,    7,   35,    5,  963, 1081,  599, 4319,
  1,    3,    1,    9,    3,   57,   11,  247,  237,  661, 1377, 1651, 4235,
  1,    1,    3,    5,   21,    9,   61,  171,  361,  523, 1747, 3951, 5421,
  1,    3,    5,   13,   15,   39,   37,   31,  489,  263, 1497, 1011, 2559,
  1,    3,    3,    7,   17,   27,   63,  199,  127,  917, 1103,  315, 4415,
  1,    1,    1,    7,   17,   41,   89,  213,   21,  103, 1789, 3513, 2439,
  1,    1,    7,    7,   31,   35,   95,   29,  345,  623,  887, 3351,  823,
  1,    1,    5,    1,    9,   61,  119,  251,  101,  231,  739, 1725, 1725,
  1,    3,    5,    1,    9,   29,  113,    7,  371,   47, 1577, 3793, 6219,
  1,    1,    7,    9,   23,   57,   67,  251,  233,  301,  313, 2399, 4903,
  1,    3,    1,    9,   19,   63,  123,  187,  431,  549, 1367,  287, 6699,
  1,    3,    5,   11,   25,   21,   91,   91,  109,  337, 1299, 4017, 5451,
  1,    3,    3,   11,    3,   31,   33,   11,  119,  675, 1801, 3571,  349,
  1,    3,    3,   15,    1,   59,   37,  149,  277,  189, 1131, 1007, 7703,
  1,    3,    1,    7,   11,   35,   99,   13,  125,  357, 1837,  541, 2927,
  1,    3,    5,    5,   27,   49,   43,  205,  263, 1005,   73, 3115, 7809,
  1,    3,    3,    5,   29,    3,   11,   37,   73,  789, 1865,  429, 6179,
  1,    3,    7,    3,    1,   49,   33,  249,  135,  189, 1065, 1585, 1417,
  1,    1,    1,   11,   31,   47,   65,  137,  123,  319,  843, 1285, 5987,
  1,    3,    7,    1,   29,   49,   81,  139,   83,  721,  635,  755, 3017,
  1,    3,    5,    3,   25,   33,   79,    9,  123, 1005,   55, 1211, 4983,
  1,    1,    1,    7,   29,   21,   81,    7,  405,  525, 1655, 3047, 3479,
  1,    3,    1,   13,    1,   19,  107,  113,   69,  675,  913,  915, 4525,
  1,    1,    3,    7,   23,   21,   63,  183,   75,  539, 1037, 3611, 4643,
  1,    1,    1,    7,   29,   35,   63,  205,  287,  191,  223, 2697, 4911,
  1,    3,    1,    7,   25,   11,   55,  187,  401,  813, 1871, 2129,  227,
  1,    3,    7,    3,   13,   17,   89,   39,   23,  917, 1161, 3669, 5475,
  1,    3,    1,   15,    3,   37,   91,    3,  283,   51,  461,   81, 2287,
  1,    1,    5,   15,   31,   23,   25,   79,  393,  167,  479, 3939, 5581,
  1,    3,    5,   11,   25,   59,   93,  155,   41,  415,  511, 2437, 6817,
  1,    3,    3,    9,    5,   13,  101,  227,  379,  579, 1721,  915, 1937,
  1,    3,    7,    3,    5,   37,   27,   89,  431,  755, 1107,  779, 1421,
  1,    3,    3,    9,   11,   35,   55,  185,   11,  605,  389, 3567, 4415,
  1,    3,    7,    3,    3,   55,   75,   51,  475,  721,  151, 3701, 7977,
  1,    1,    5,   15,   21,   57,  121,  127,  505,  837,   35, 2479, 1789,
  1,    3,    3,   13,    9,    1,   79,   63,   19,  529,  375, 3807, 3907,
  1,    3,    1,    5,   23,   29,   43,   83,  365,   31, 1099, 1893, 6815,
  1,    3,    1,    3,    7,   45,  125,   41,  265,  327,  937, 3927, 6789,
  1,    1,    3,    3,   11,   11,   73,  133,  271,  799, 1185, 2619, 6003,
  1,    1,    1,    3,   23,    1,   27,  183,  499,  961, 1701, 2543, 5609,
  1,    1,    3,    5,   11,   15,  109,  181,  489,  279,  769, 3633, 4507,
  1,    3,    5,    9,    1,    9,   35,  127,  443,  409,  639, 2007,  337,
  1,    3,    5,   15,    1,   33,   21,   19,  165,  847, 1633, 3857, 7427,
  1,    1,    7,    9,    3,   19,   71,  255,   91,  649, 1609, 3837, 7943,
  1,    3,    5,    9,   23,   53,  113,  219,   83,  241,  379,  487, 3075,
  1,    3,    3,    1,   25,   43,   89,   59,  291,  285, 1613, 1769, 6427,
  1,    1,    7,    5,   23,   39,   59,  251,  319,  545, 2031, 3759, 1019,
  1,    3,    7,    9,    1,   23,   95,    3,  199,  407,  685, 3105, 7121,
  1,    1,    7,    9,   23,    7,   41,  187,  107,  161,  289, 2727, 4763,
  1,    3,    3,   15,    3,   13,   45,   57,  245,  591,  975, 3155,   81,
  1,    1,    7,    5,   27,   13,  113,  217,  389,   73,  671, 2479, 3587,
  1,    3,    3,   15,    9,    1,  119,  115,  143,  313, 1599, 1341, 2929,
  1,    1,    7,    7,   27,   19,  113,  217,  137,  811, 1447, 1657, 1795,
  1,    3,    1,    9,    3,   41,   39,  229,   89,   17,  871, 2767, 8067,
  1,    3,    3,    1,   23,   55,   59,  181,  125,  663,  647, 2541, 2415,
  1,    3,    1,    9,   25,    1,   73,  185,  281,  269,   99,  577, 1265,
  1,    3,    7,    9,   19,   13,   15,  149,  381,  261,  139, 2105, 4025,
  1,    3,    7,    5,   29,   15,   13,   83,  215,   37, 1427,  799, 5599,
  1,    3,    1,   11,   29,   59,   59,  115,  131,  783,  959,   17, 4771,
  1,    1,    7,    5,   13,   55,   67,   11,  299,  127,   89, 2871, 3025,
  1,    1,    3,   15,   27,   15,  121,  123,  249,  917,  117, 3637, 2313,
  1,    3,    7,   15,    5,    3,   27,   19,  375,  231,  841,  953, 6129,
  1,    1,    3,   11,    9,   57,    7,  109,  455,  577,  891,   65, 7611,
  1,    3,    7,    7,   29,   37,  105,  165,   43,  975, 1959,   69, 6881,
  1,    1,    3,    7,   29,   31,   15,  103,   73,  793,  223, 2897, 5253,
  1,    1,    7,    7,   13,   17,   59,  123,  281,  921, 1697, 3841, 4413,
  1,    1,    3,    1,   17,    1,   59,  219,  217,  343, 1145, 3559, 7869,
  1,    1,    5,    1,    3,    3,   35,  129,  297,  751,  499, 4067,  105,
  1,    1,    1,   11,   23,   21,   91,  155,  229,  139, 1435, 2335, 3173,
  1,    3,    1,   11,   19,   29,   89,  207,  431,  221, 1809, 3409, 1629,
  1,    1,    7,   13,    7,   25,   23,  177,  357,   79, 1413, 1087, 2537,
  1,    1,    3,   15,   13,   55,  125,    9,   81,  817, 1445,  425, 1023,
  1,    1,    1,    3,    3,    9,   97,   49,  357,  393, 1675, 2813, 4409,
  1,    3,    5,   13,   19,   37,   53,  181,  171,  545,  171, 1705, 7209,
  1,    1,    5,    5,   23,   33,   41,  231,  451,   11, 1073, 1701, 4413,
  1,    3,    7,    1,    5,   53,   91,   33,  481,  781, 1349, 1237, 7107,
  1,    1,    1,    7,   29,   41,  111,  233,   13,   71, 1545,  821, 7469,
  1,    1,    5,    1,   29,   51,   29,   67,  387,    1, 2039, 1375,   33,
  1,    3,    5,   11,   13,   19,   31,  155,  491,  699, 1027, 3673, 1955,
  1,    3,    5,    3,   13,   57,    3,   41,  489,  767, 1563, 2693, 2881,
  1,    3,    7,   13,    5,   13,  103,    9,  439,  917,  859, 3925, 5167,
  1,    1,    1,   15,   19,   63,   61,   95,  385,    9,  215, 1541, 6451,
  1,    3,    5,    3,    5,   43,   71,  123,  487,  107, 1673, 1871, 4211,
  1,    1,    5,    5,   17,   19,   35,   65,  177,  341, 1919, 2285,  179,
  1,    3,    1,    3,    9,    7,    7,  117,  393,  587, 1633,  847, 5573,
  1,    1,    5,    5,   11,   13,  119,  249,   33,  903,  779, 4035, 7879,
  1,    1,    5,    7,   11,   37,   29,   85,   71,  965,  411, 1101, 3387,
  1,    3,    3,    3,   29,   33,   45,  169,  375,  599, 1845, 2029, 7759,
  1,    1,    1,    9,   27,   19,   49,  129,  443,  507, 1477,  855, 5455,
  1,    3,    3,    9,   23,   15,  111,  241,  129,  843, 1489, 2733, 7157,
  1,    3,    1,    5,   19,   63,   41,  173,  407,  739,  447, 2503, 1891,
  1,    1,    7,    1,   17,   51,  109,  251,  395,  579, 1545,  121, 5683,
  1,    3,    3,    7,   25,   11,   59,  225,  127,  397,  351, 2855, 5689,
  1,    1,    1,   11,   13,   49,  125,  147,   65,  397, 1989, 1069, 6535,
  1,    3,    3,    9,    1,   23,   13,  165,  333,  325,  495, 3463, 3109,
  1,    3,    5,    3,   13,   57,   27,   69,  309,  775,  183, 3505, 6555,
  1,    1,    7,    5,    3,   47,   19,   81,  119,  565, 1639, 1539, 6873,
  1,    3,    7,   11,   11,   51,   79,  239,  197,  925, 1385,  607, 1249,
  1,    3,    7,   13,    1,   15,    9,   95,  435,   75, 1805, 1349, 4251,
  1,    1,    1,   13,   17,   53,   75,   23,  497,   55, 1097,  575, 6437,
  1,    3,    1,   13,   29,   41,   83,   83,  373,  979, 1249, 2301,   49,
  1,    3,    7,    9,    1,    1,   81,  227,   71,  931, 1431, 2321, 2745,
  1,    3,    3,   15,   13,   15,   33,  249,  379,   93, 1571, 1101, 1201,
  1,    3,    1,    5,   17,   37,   91,  143,  509,  957,  591,  333, 7327,
  1,    3,    5,    7,    9,   61,  109,  171,  387,  857,  697,  291, 4179,
  1,    3,    5,    1,   17,   11,   33,  193,  159,  753, 1509, 2171, 6783,
  1,    1,    5,   15,   21,   35,   29,    9,  265,  965,  709, 4085,  623,
  1,    3,    1,   11,    1,   29,  107,   21,  477,  795,   31, 2173, 2779,
  1,    1,    1,    9,   11,   33,  111,   57,  463,   67, 1563, 2541, 5963,
  1,    1,    1,   15,    1,   23,  101,   73,  449,    5,  165, 1195, 2585,
  1,    3,    1,   15,    1,   55,  107,   97,   47,   87,  513,  925, 6927,
  1,    3,    1,   13,   25,   11,  109,   57,  353,  909, 1425, 4039, 5333,
  1,    3,    5,   13,    5,   59,   65,   29,  249,   97, 1299, 1379, 4033,
  1,    1,    3,   13,    7,   19,   59,  239,  335,  995, 1081,  699,  285,
  1,    1,    5,    1,   29,   61,   43,  151,  505,  271,  145, 1979, 7467,
  1,    3,    1,   11,   29,   61,   37,  159,   89,  875, 1841,  275, 4443,
  1,    3,    3,    9,   19,   45,    1,  191,  141,  671, 1211,  953, 4917,
  1,    3,    5,   15,   19,   13,    9,   47,   55,  613,  941, 1755,    3,
  1,    3,    3,    9,    1,   49,   15,   51,  235,   33,  609, 1643, 4319,
  1,    3,    1,    5,   29,   13,  109,    1,  187,  351,  845,  325, 5517,
  1,    3,    1,   15,   13,   63,   37,  223,   87,   69, 1169,  101, 3449,
  1,    3,    1,    5,    3,    5,  111,  251,  363,  811, 1865, 2263,  813,
  1,    1,    1,    7,    1,   61,  113,  251,   93,  669, 1593, 3329, 5499,
  1,    3,    3,    3,   31,    5,  119,  151,  363,  729,  347, 3673, 2515,
  1,    3,    7,   11,   15,   31,   79,   41,  101,  401,  293, 3413, 5771,
  1,    3,    3,    3,   13,   17,   73,  119,   67,  647, 1277, 1977, 3357,
  1,    3,    7,   15,    3,   61,   65,  127,  215,  241,  157, 2727, 2073,
  1,    1,    5,    7,    1,   63,   71,  131,  321,  435,  211, 2313, 4395,
  1,    3,    7,   13,   11,   13,   93,   33,  331,  447,   93, 1419, 4925,
  1,    1,    1,   11,   19,   27,   17,  209,  305,  721, 1679,  887, 2643,
  1,    3,    5,    7,    5,   57,  101,  123,  261,  271, 1799,  609, 7215,
  1,    3,    5,    3,   29,    1,   87,   53,  411,  745,  527, 2475, 5817,
  1,    3,    7,    7,   13,   21,   97,  241,  491,   53,   41,  591, 1199,
  1,    1,    5,   13,   29,    5,   43,   25,  479,  775,  473, 2613, 1597,
  1,    3,    3,    5,   23,   11,   23,   31,   65,   99,  563, 2081, 1619,
  1,    1,    3,   13,    3,   39,   75,  183,  307,  343,  187, 3805, 7535,
  1,    3,    7,   15,    1,   57,  109,  107,  469,  451, 1525, 3435, 4833,
  1,    1,    5,    5,   31,   51,   41,   25,  415,  427,  575, 2409,  609,
  1,    1,    3,   13,   13,   53,   49,  115,  131,  593, 1579,  111, 4797,
  1,    1,    1,    9,   19,   39,   53,   39,  315,  339,  857, 3557, 8171,
  1,    3,    1,    1,   17,   25,   31,   11,  487,  845,  703, 3607, 6847,
  1,    3,    3,   15,    5,   41,   97,  213,   83,  243, 1211,  903,  793,
  1,    1,    1,   11,    5,   39,  105,  239,  455,  345,  647,  231, 6757,
  1,    3,    3,    5,    1,   37,  109,  219,   19,   17,  709, 3059, 8165,
  1,    1,    1,    5,   29,   23,  119,  109,  113,  573,  981,  473, 3371,
  1,    1,    1,    1,   23,   31,   51,  185,  163,  421,  285, 2959, 2431,
  1,    3,    3,   11,    3,   25,    9,   35,  503,  517,  697, 2925, 5235,
  1,    3,    7,    3,   19,   33,   53,  133,   99,  971,  163, 3861, 4739,
  1,    1,    1,    3,   25,   17,  113,  123,  499,  499,  981, 2043, 7703,
  1,    3,    7,    7,   19,   57,   97,  185,  251,  435,  153, 3887, 7223,
  1,    1,    1,    1,   27,   29,   73,   27,  239,  769, 1515,  351, 6525,
  1,    1,    1,    9,    9,   27,   89,   55,   81,   75,   47, 2865, 5891,
  1,    1,    5,    7,   27,   23,   79,  245,  167,  203, 1553,  369, 5605,
  1,    1,    1,   15,   13,   47,   49,   61,  391,  793,  599, 1377, 4433,
  1,    3,    7,    9,   15,   41,   61,   75,  255,  985,  225, 2639, 3533,
  1,    1,    5,    9,   29,   29,  105,  205,  317,  343, 1147, 1261, 5267,
  1,    3,    3,    3,   23,   19,   13,  213,  363,  955,  381, 3625, 5125,
  1,    1,    7,   11,   13,   47,   99,  169,  359,  735,  135, 3279, 5037,
  1,    1,    3,   15,   25,   41,   53,  163,  395,  523,  821, 2201,  225,
  1,    3,    5,    7,   25,   25,   71,   63,  419,  659, 1965, 2949, 6717,
  1,    1,    3,    1,   17,    5,    7,   55,  307,  703,  609, 3049, 1121,
  1,    3,    1,    3,   19,   51,   87,   49,  251,  303, 1033,  449, 5741,
  1,    1,    1,    1,   17,   43,   21,   83,  267,  421,  983, 1297, 2013,
  1,    3,    5,    1,   15,   39,  101,  195,  171,  951,  503,  897, 4327,
  1,    3,    5,    1,   27,   29,    5,   51,  461,  405, 1117, 1891, 4839,
  1,    3,    1,    9,    3,    7,   71,   31,  183,  631,  327,  411,  569,
  1,    3,    7,    1,   25,   31,   31,   41,  465,  825,  453, 2773, 5227,
  1,    3,    7,    5,   17,   45,  123,   15,  165,  735, 2005,  749, 7677,
  1,    3,    3,   15,   27,   51,  121,  203,  163,  433, 1257, 2753, 4315,
  1,    1,    7,   15,    3,   49,  121,   41,  293,  841,  343, 1825, 2391,
  1,    3,    3,    7,   27,   55,   73,   63,  477,  485, 1649,  853, 5551,
  1,    3,    7,    5,   31,   17,   79,  127,  223,   49, 1199, 2775,  859,
  1,    3,    1,    5,   23,   43,  115,  161,  403,  749,  599, 3547, 3627,
  1,    3,    5,    7,   13,   49,   13,    5,  389,  107, 1877, 3923, 6377,
  1,    1,    1,    9,   31,   45,   39,  143,   97,  669,  569, 3923, 3903,
  1,    3,    5,    7,   11,    9,  101,    7,  335,  211,  695,  987, 4311,
  1,    3,    3,   15,   15,   29,   19,  199,  357,  497, 1587, 3723, 6527,
  1,    1,    7,   13,    7,    3,   37,  251,  297,  143, 1475, 2189, 7573,
  1,    3,    3,   13,   21,    5,   51,   95,   19,   99,  187, 3877, 4905,
  1,    3,    5,   11,   19,   47,   83,   75,  469,   57,  973, 3577, 7731,
  1,    3,    7,    1,   27,    9,   97,  101,  501,  277,  233,  297, 1909,
  1,    3,    7,    9,   19,   15,   55,   15,  249,  969,  511, 2763, 1555,
  1,    3,    7,   11,   21,   19,   81,   43,   85,  107,   51, 1845, 3279,
  1,    1,    3,    1,   29,   51,   91,  237,  213,  397, 1083, 3083, 1949,
  1,    1,    3,   13,    7,   45,  127,  197,  311,  563,  665, 2951, 1887,
  1,    1,    1,    1,   31,   57,  105,  117,  265,  551, 1321,  483, 6675,
  1,    1,    1,    7,   13,   63,   89,  167,  379,  447,  531, 2169, 5509,
  1,    3,    5,   15,    9,    9,   63,  155,  297,  381, 1875, 3985, 2033,
  1,    3,    5,   15,    9,   21,   47,   21,  283,  187, 1939,  245, 5473,
  1,    3,    3,    5,    7,   59,   49,   83,  393,   57,  859, 3655, 3539,
  1,    1,    7,    5,   21,    3,   75,  205,  449,  405, 1507, 3441, 5033,
  1,    3,    1,    1,   13,    9,   37,  255,  463,  731, 1979, 1023, 5935,
  1,    3,    1,   11,   11,   13,   77,   49,  289,  769, 1203,  235, 6095,
  1,    1,    1,    3,    9,   45,   15,  101,  159,  923, 1965,  835, 4761,
  1,    1,    3,    9,   11,   23,   49,  213,  289,  955,  737, 3693, 1771,
  1,    3,    5,   11,   29,   15,  107,  237,  499,  915,  921, 3585, 1271,
  1,    3,    3,    9,   19,   31,   23,  135,  407,  737, 1565,  327, 1717,
  1,    1,    1,    9,   11,   21,   23,  135,  129,  595, 1943, 1003, 4415,
  1,    1,    1,    9,   19,   15,   35,   21,  137,  341,  819,  543, 5083,
  1,    3,    3,    1,   21,   51,   19,   73,  221,  253,  223, 3059, 6277,
  1,    3,    3,    9,    5,   35,   69,   93,   43,  823,  365, 2637, 3147,
  1,    1,    7,    3,   29,    9,   17,  115,   89,  197,  167, 2923, 7695,
  1,    3,    5,    5,   13,   11,   59,    7,  403,  321, 1705,   87, 2461,
  1,    1,    1,   15,    7,   61,   63,   85,  271,  315,  413, 3617, 4783,
  1,    1,    1,    1,   19,   23,   73,  223,   75,  181, 1577, 1031, 4539,
  1,    3,    3,    1,   19,   53,   29,  237,   83,  885,  745, 1043, 5833,
  1,    1,    7,    9,   27,   29,  125,   79,  445,  497, 1573,  903, 5583,
  1,    3,    1,    7,   23,   51,   61,   89,  453,  159,  655, 2913,  651,
  1,    3,    5,    3,   31,   45,   65,    5,  389,  571, 1633, 2177, 1419,
  1,    3,    7,    3,    1,   31,   95,   57,  149,  981, 1003, 2641, 2605,
  1,    3,    3,    1,   27,   29,  101,  239,  143,  899,   91, 3279, 5511,
  1,    3,    7,    9,   21,    5,   81,   67,  423,  785, 1123,  389, 3913,
  1,    1,    5,    9,    7,   35,   57,   65,  499,  947,  477, 2009, 5795,
  1,    3,    5,   11,    3,   29,   69,  201,  317,  217, 1741,  525, 2333,
  1,    1,    7,    9,    7,   53,   83,  155,  445,  217, 1663, 4085, 2329,
  1,    1,    3,    9,   11,   35,   37,   71,  157,  135,   35, 3299, 4431,
  1,    3,    5,   13,   23,   17,   11,   85,  137,  753,  715,  987, 3725,
  1,    3,    3,   13,   13,   59,   37,  195,  453,  623,   37, 2409, 6069,
  1,    3,    1,    3,   29,   55,   95,   89,  163,  565, 1513,  813, 2699,
  1,    3,    5,   13,   11,   27,    1,  181,   87,  717,  815, 2683, 7055,
  1,    1,    3,   11,   31,   51,   73,  119,   23,  903,  941,  373, 6879,
  1,    3,    1,   13,   19,   59,   27,  135,  391,  581, 1379, 2695, 1017,
  1,    1,    1,    5,    1,   27,   29,  147,  119,  955,  263, 3775, 3121,
  1,    1,    7,    1,    5,   47,   57,  237,  427,  621, 1831, 2375, 2547,
  1,    3,    5,    5,    5,   15,    7,  173,  323,  361, 1735, 1119, 4603,
  1,    3,    1,    5,   11,   29,   65,   41,  173,  869, 1111, 2791, 2385,
  1,    3,    7,    9,    5,   37,   83,  155,   89,   87, 1449,  223, 6915,
  1,    3,    3,    9,    3,    7,   99,   67,  259,  943,  353,  325, 6103,
  1,    3,    7,    3,   27,   49,   69,  113,  377,  907, 1941,  587, 5669,
  1,    3,    5,   13,    5,   55,   19,  111,  511,  853, 1655, 1379, 7833,
  1,    1,    1,   13,    7,    5,  103,   21,  249,  353, 1349, 2877, 2001,
  1,    1,    7,    9,   11,   19,   43,  183,   31,  335,  877, 2867, 4287,
  1,    3,    1,   15,   31,   45,   95,   23,  363,  197,  285, 3793, 6619,
  1,    1,    7,    9,    1,   29,   25,  103,  229,  771, 1723,  655,  955,
  1,    3,    7,   11,   27,   19,   19,  207,  353,  433,  125,  831, 2761,
  1,    1,    1,    7,   31,   57,  103,  253,  329,  743, 1753, 3425, 5711,
  1,    1,    1,   11,   31,   33,   41,   69,  493,  195,  985, 1663, 6291,
  1,    3,    7,    9,   23,   53,  125,  219,  427,   91,  723, 1681, 3415,
  1,    1,    1,   13,    5,   45,   97,  205,   57, 1023,  175, 2657, 3909,
  1,    1,    5,    9,   21,   21,   71,  195,  205,   63,  439, 1865, 2841,
  1,    1,    5,    1,   27,    9,  105,   43,  389,  301,  791, 3943, 5627,
  1,    1,    1,   15,    9,    3,   83,  197,   91,  647, 1051, 2977, 4939,
  1,    3,    1,    9,   25,   35,   83,  229,   83,  205, 1261, 1979, 7671,
  1,    3,    7,    7,    3,   29,   61,  139,   13,  485,  717, 2271, 6059,
  1,    1,    5,    7,   15,   43,   39,  177,  219,  927, 1555, 3247, 6275,
  1,    1,    7,    1,   19,   31,    9,  129,  439, 1003, 1757, 1267, 6517,
  1,    3,    1,    7,    1,   39,   45,   69,   45,  987, 1777, 1747, 1931,
  1,    1,    5,    9,   19,    3,  117,   97,   35,  359,  577,  811, 4583,
  1,    1,    3,    9,    9,   45,   63,  201,  371,  577, 1583,  159, 7301,
  1,    1,    5,   15,    5,    1,   31,  163,  441,  147, 1957,  429, 1267,
  1,    3,    3,    1,   25,   41,    5,  189,   17,  141,  873, 2001, 7509,
  1,    1,    3,   11,   21,   29,  117,   11,  267, 1017,  331, 1195, 1435,
  1,    3,    7,    1,   15,    5,   67,   99,  501,  701, 1163, 3065, 2169,
  1,    1,    1,   13,   25,   59,  125,   91,   53,  273,  313,  553, 6939,
  1,    1,    5,   13,   29,   41,   41,  253,   25,   89,    1, 1499, 3515,
  1,    3,    1,   15,   15,   33,  117,  239,  333,  589, 1963, 3529, 2985,
  1,    3,    1,    9,   21,   35,   43,   91,   17,  487,  963, 1081, 2787,
  1,    1,    5,   13,   11,   27,   77,  145,  201,  859, 1905, 2877, 2123,
  1,    3,    5,    7,   19,   19,   97,   19,  475,  343,  821, 3077, 1969,
  1,    1,    3,   15,   15,   13,   15,  179,  257,   91, 1677,  845, 3307,
  1,    1,    3,    3,    3,   25,   29,  231,  417,  847,  185, 1793,  353,
  1,    3,    7,    9,    7,   27,    5,  121,  345,  341,  709, 2409, 4359,
  1,    3,    5,    3,   13,   43,   59,    7,  381,  173,  545, 3995, 7059,
  1,    3,    5,    1,   11,   33,   25,  225,  377,  287, 1723, 2559, 5273,
  1,    3,    1,   13,   25,   35,   63,  237,   55, 1003,  215, 4081, 5873,
  1,    3,    1,    7,   17,   17,   87,  125,  403,  289, 1885, 1195, 6657,
  1,    1,    1,    5,    1,   17,   39,  191,   77,  639, 1249, 2955, 6765,
  1,    3,    3,    9,    5,   23,   39,  119,  389,  983,  583, 1117, 6229,
  1,    1,    1,    3,   31,    7,   77,   59,  347,  685, 1803, 1409, 3179,
  1,    1,    5,    1,   13,   35,   85,  175,  363,  697,  839,  785, 1583,
  1,    1,    7,    7,   29,   15,   37,  237,  211,   35,  885,  287, 6237,
  1,    3,    7,    1,   23,   61,   81,  131,  413,  701,  485, 1521, 2155,
  1,    1,    1,    1,    9,   61,   73,   79,  419,  645,  413, 1607,  371,
  1,    1,    7,   13,    5,   53,   89,   43,    5,  911, 1767,   85,  273,
  1,    1,    5,    3,   29,    5,   29,   45,  167,  501,  425, 3055, 7491,
  1,    3,    7,    3,    7,   15,  125,  205,  219,  705,  129, 3123, 3309,
  1,    1,    3,   11,   17,   23,  109,  199,  201,  873, 1035, 2533, 6805,
  1,    1,    7,    1,   27,   11,   21,  251,  285,  763,  329, 2329, 3015,
  1,    3,    3,    7,    7,   13,   23,  153,  425,  745, 1263, 3477, 6831,
  1,    1,    1,   13,   17,   43,  119,  207,   11,  657, 1881,  799, 7819,
  1,    3,    3,   15,   31,   55,  105,   37,   77,  559, 1779, 3683,  713,
  1,    3,    7,   15,    9,   47,   43,  179,  269,  699, 1565, 3715, 4747,
  1,    3,    3,    5,   31,   25,   93,  113,  489,  315,  359,  337, 3935,
  1,    3,    1,    7,    9,   43,   97,  255,  281,  347,  367, 3139, 4109,
  1,    3,    5,   13,    9,   15,   15,  107,  403,  429,  453, 3311, 1311,
  1,    1,    5,   13,    7,   57,  125,  217,   79,  197,  707,  431,  709,
  1,    1,    3,   15,   21,   45,   29,   61,  425,  165, 1419, 3511, 3089,
  1,    1,    5,   11,    3,    1,   51,    7,  125,  955,  831, 2299, 7059,
  1,    3,    1,   13,    3,   49,   69,  181,   81,  859, 1889,  365, 4247,
  1,    3,    3,    1,    3,   63,   37,  247,  331,  167,  887, 2941, 2989,
  1,    3,    5,   13,    9,   57,   45,   31,  437,  303, 1871, 3067, 1509,
  1,    3,    5,   13,   11,   15,   31,   13,  271,  833, 1869, 1331, 4919,
  1,    1,    5,    3,   21,   31,   75,  113,  397,  531,  747, 1081, 1841,
  1,    3,    1,    9,   11,   31,  109,  145,  299,  473,  223, 1097, 3045,
  1,    3,    1,   15,   31,    7,  119,  107,  475,  635, 1547, 2853, 3821,
  1,    3,    7,   15,    9,   53,   53,  233,  271,  641, 1799, 2299, 6929,
  1,    3,    7,   11,   25,   27,    5,  233,  249,  195,  433,  495, 4655,
  1,    1,    1,   15,    5,   15,  101,   43,  413,  589, 1441, 1745, 1333,
  1,    1,    5,    9,    1,   47,  125,   79,  233,  821,  553,  749, 6429,
  1,    3,    5,   15,   31,   23,  121,   23,  261,  205, 2021, 3819, 6649,
  1,    3,    1,    1,   13,    7,   35,  169,  495,    3, 1303,  619, 2131,
  1,    3,    3,   13,   29,   29,   29,  137,  171,  635, 1505, 1059, 5265,
  1,    1,    5,   15,    9,   53,    7,  129,   69,  371, 1735, 3559, 1051,
  1,    3,    1,    1,   29,   47,   63,  183,   27,  891, 1619,  183,  261,
  1,    1,    5,    1,    1,    9,   17,   53,  409,  249, 1065, 3743, 8057,
  1,    1,    3,    5,   11,   53,   63,   91,   21,  123, 1161,  723, 3379,
  1,    3,    5,   11,   19,    3,   13,   55,  421,   77, 2047,  949, 2179,
  1,    3,    3,    5,    7,   25,   69,  103,  367,  623,  347, 3501, 1993,
  1,    1,    3,    1,   27,   55,   15,  223,   81,  993,  867,  733, 5655,
  1,    3,    7,   11,   13,   45,  105,   87,  483,  401,  881, 2599, 3063,
  1,    3,    5,   11,   31,   63,   51,  177,  255,  525, 1447, 3983, 6381,
  1,    1,    7,    5,    7,   21,  127,  157,   15,  427,  329, 3961, 3587,
  1,    1,    3,    3,   31,   17,  105,   79,  219,   71,  781,  911, 7417,
  1,    1,    7,    9,    7,   23,    9,  213,  365,  655, 1065, 1899, 1579,
  1,    1,    3,    1,   25,   31,   57,  139,  497,  951,  219,  985, 1541,
  1,    1,    1,    3,   23,   27,   95,  183,  181,  357,  589, 2493, 2107,
  1,    3,    3,    5,   21,   27,   59,  231,   75,  851,  645, 1795, 5085,
  1,    1,    7,   13,   29,   43,  109,  205,  431,  899, 1257,  653, 2873,
  1,    1,    7,    9,   11,   63,   35,  143,   99,  535, 1833,  157, 6141,
  1,    3,    3,    7,   11,   55,   49,  129,  325,  493,  749,  433,  955,
  1,    3,    3,    7,   13,   63,   23,  243,  407,  323, 1841, 2361, 3537,
  1,    1,    1,    1,   11,   45,   33,  205,  229, 1003, 1733, 3093, 2157,
  1,    1,    1,    9,   27,   51,  107,   93,  281,  343, 1179, 3119,  841,
  1,    1,    3,    9,    1,   15,   55,   59,   63,  515, 1191, 3679, 1999,
  1,    3,    3,   15,   23,   27,   33,   15,   83,  859, 1025, 2367, 1465,
  1,    1,    3,    7,   31,    5,   57,   89,  493, 1017, 1639, 1701, 5171,
  1,    1,    3,    5,   21,   37,   79,    9,    5,    5, 1955, 1445, 5651,
  1,    3,    3,    5,   23,   43,   73,   11,  113,  423, 1423, 1321, 1535,
  1,    3,    5,   15,   21,   11,   69,   47,   15,  315, 1685, 2397, 7235,
  1,    1,    5,   13,   19,   27,   59,  133,  271, 1011, 1711, 1241, 4349,
  1,    3,    3,    9,   31,    5,  107,  227,   37,  703,  493, 3305, 1263,
  1,    3,    3,    7,    5,   27,   55,   75,   87,   41,  549, 3985, 1453,
  1,    3,    3,   13,   31,   59,   11,    9,  451,  777,  783, 2349, 1005,
  1,    3,    1,    3,   25,   21,   63,   91,  299,  163, 1653, 4067, 6893,
  1,    3,    3,   13,   25,    7,   95,   19,   83,   95,  397, 3805, 2919,
  1,    3,    5,   11,   19,   39,  103,  171,  451,  831,  895, 3073, 1947,
  1,    3,    7,   13,   17,   27,   23,  163,  311,   79,  233, 2837, 1635,
  1,    3,    7,    7,   11,   63,  125,   79,  441,  975,  759, 1567, 3963,
  1,    1,    1,    9,   25,   35,   91,    7,   47,  235, 1505, 3783,  397,
  1,    1,    5,   13,    7,   47,   31,  103,  455,  633,  677,  451,  969,
  1,    3,    7,   13,   13,   55,   91,    5,   47,  723, 1449, 2441, 4569,
  1,    3,    3,   13,    1,   17,   51,  119,  253,  297, 1573, 1181,  655,
  1,    1,    7,   15,   29,   17,   65,  155,   13,  589, 1297,  487, 6737,
  1,    1,    1,    9,   17,   17,   61,   75,  109,  317, 1821,  543, 2995,
  1,    3,    1,    5,   23,    3,   75,   11,  369,  679, 1691, 1201, 7235,
  1,    1,    3,    5,   15,   19,   69,   71,  347,  981,  791, 3735, 7713,
  1,    3,    5,    3,    7,   21,  107,   95,   11,  195,  289, 2517,  973,
  1,    3,    7,    3,   29,   13,   65,   17,  409,  399, 1187,  733, 4821,
  1,    3,    5,    3,   17,   49,  101,   13,  275, 1003,  867, 1535, 2377,
  1,    3,    3,    1,   13,   61,   59,  243,   63,  121, 1535, 2175, 1673,
  1,    3,    3,    3,    3,   39,   35,  207,  441,  501,  575, 3613,    1,
  1,    1,    3,   15,   17,   15,   15,  187,   15,  155,  183, 3019, 6541
} ;

const Unsigned64BitsInteger SobolSequence::PrimitivePolynomial[MaximumDimension] =
{
  1,     3,     7,    11,    13,    19,    25,    37,
  59,    47,    61,    55,    41,    67,    97,    91,
  109,   103,   115,   131,   193,   137,   145,   143,
  241,   157,   185,   167,   229,   171,   213,   191,
  253,   203,   211,   239,   247,   285,   369,   299,
  301,   333,   351,   355,   357,   361,   391,   397,
  425,   451,   463,   487,   501,   529,   539,   545,
  557,   563,   601,   607,   617,   623,   631,   637,
  647,   661,   675,   677,   687,   695,   701,   719,
  721,   731,   757,   761,   787,   789,   799,   803,
  817,   827,   847,   859,   865,   875,   877,   883,
  895,   901,   911,   949,   953,   967,   971,   973,
  981,   985,   995,  1001,  1019,  1033,  1051,  1063,
  1069,  1125,  1135,  1153,  1163,  1221,  1239,  1255,
  1267,  1279,  1293,  1305,  1315,  1329,  1341,  1347,
  1367,  1387,  1413,  1423,  1431,  1441,  1479,  1509,
  1527,  1531,  1555,  1557,  1573,  1591,  1603,  1615,
  1627,  1657,  1663,  1673,  1717,  1729,  1747,  1759,
  1789,  1815,  1821,  1825,  1849,  1863,  1869,  1877,
  1881,  1891,  1917,  1933,  1939,  1969,  2011,  2035,
  2041,  2053,  2071,  2091,  2093,  2119,  2147,  2149,
  2161,  2171,  2189,  2197,  2207,  2217,  2225,  2255,
  2257,  2273,  2279,  2283,  2293,  2317,  2323,  2341,
  2345,  2363,  2365,  2373,  2377,  2385,  2395,  2419,
  2421,  2431,  2435,  2447,  2475,  2477,  2489,  2503,
  2521,  2533,  2551,  2561,  2567,  2579,  2581,  2601,
  2633,  2657,  2669,  2681,  2687,  2693,  2705,  2717,
  2727,  2731,  2739,  2741,  2773,  2783,  2793,  2799,
  2801,  2811,  2819,  2825,  2833,  2867,  2879,  2881,
  2891,  2905,  2911,  2917,  2927,  2941,  2951,  2955,
  2963,  2965,  2991,  2999,  3005,  3017,  3035,  3037,
  3047,  3053,  3083,  3085,  3097,  3103,  3159,  3169,
  3179,  3187,  3205,  3209,  3223,  3227,  3229,  3251,
  3263,  3271,  3277,  3283,  3285,  3299,  3305,  3319,
  3331,  3343,  3357,  3367,  3373,  3393,  3399,  3413,
  3417,  3427,  3439,  3441,  3475,  3487,  3497,  3515,
  3517,  3529,  3543,  3547,  3553,  3559,  3573,  3589,
  3613,  3617,  3623,  3627,  3635,  3641,  3655,  3659,
  3669,  3679,  3697,  3707,  3709,  3713,  3731,  3743,
  3747,  3771,  3791,  3805,  3827,  3833,  3851,  3865,
  3889,  3895,  3933,  3947,  3949,  3957,  3971,  3985,
  3991,  3995,  4007,  4013,  4021,  4045,  4051,  4069,
  4073,  4179,  4201,  4219,  4221,  4249,  4305,  4331,
  4359,  4383,  4387,  4411,  4431,  4439,  4449,  4459,
  4485,  4531,  4569,  4575,  4621,  4663,  4669,  4711,
  4723,  4735,  4793,  4801,  4811,  4879,  4893,  4897,
  4921,  4927,  4941,  4977,  5017,  5027,  5033,  5127,
  5169,  5175,  5199,  5213,  5223,  5237,  5287,  5293,
  5331,  5391,  5405,  5453,  5523,  5573,  5591,  5597,
  5611,  5641,  5703,  5717,  5721,  5797,  5821,  5909,
  5913,  5955,  5957,  6005,  6025,  6061,  6067,  6079,
  6081,  6231,  6237,  6289,  6295,  6329,  6383,  6427,
  6453,  6465,  6501,  6523,  6539,  6577,  6589,  6601,
  6607,  6631,  6683,  6699,  6707,  6761,  6795,  6865,
  6881,  6901,  6923,  6931,  6943,  6999,  7057,  7079,
  7103,  7105,  7123,  7173,  7185,  7191,  7207,  7245,
  7303,  7327,  7333,  7355,  7365,  7369,  7375,  7411,
  7431,  7459,  7491,  7505,  7515,  7541,  7557,  7561,
  7701,  7705,  7727,  7749,  7761,  7783,  7795,  7823,
  7907,  7953,  7963,  7975,  8049,  8089,  8123,  8125,
  8137,  8219,  8231,  8245,  8275,  8293,  8303,  8331,
  8333,  8351,  8357,  8367,  8379,  8381,  8387,  8393,
  8417,  8435,  8461,  8469,  8489,  8495,  8507,  8515,
  8551,  8555,  8569,  8585,  8599,  8605,  8639,  8641,
  8647,  8653,  8671,  8675,  8689,  8699,  8729,  8741,
  8759,  8765,  8771,  8795,  8797,  8825,  8831,  8841,
  8855,  8859,  8883,  8895,  8909,  8943,  8951,  8955,
  8965,  8999,  9003,  9031,  9045,  9049,  9071,  9073,
  9085,  9095,  9101,  9109,  9123,  9129,  9137,  9143,
  9147,  9185,  9197,  9209,  9227,  9235,  9247,  9253,
  9257,  9277,  9297,  9303,  9313,  9325,  9343,  9347,
  9371,  9373,  9397,  9407,  9409,  9415,  9419,  9443,
  9481,  9495,  9501,  9505,  9517,  9529,  9555,  9557,
  9571,  9585,  9591,  9607,  9611,  9621,  9625,  9631,
  9647,  9661,  9669,  9679,  9687,  9707,  9731,  9733,
  9745,  9773,  9791,  9803,  9811,  9817,  9833,  9847,
  9851,  9863,  9875,  9881,  9905,  9911,  9917,  9923,
  9963,  9973, 10003, 10025, 10043, 10063, 10071, 10077,
  10091, 10099, 10105, 10115, 10129, 10145, 10169, 10183,
  10187, 10207, 10223, 10225, 10247, 10265, 10271, 10275,
  10289, 10299, 10301, 10309, 10343, 10357, 10373, 10411,
  10413, 10431, 10445, 10453, 10463, 10467, 10473, 10491,
  10505, 10511, 10513, 10523, 10539, 10549, 10559, 10561,
  10571, 10581, 10615, 10621, 10625, 10643, 10655, 10671,
  10679, 10685, 10691, 10711, 10739, 10741, 10755, 10767,
  10781, 10785, 10803, 10805, 10829, 10857, 10863, 10865,
  10875, 10877, 10917, 10921, 10929, 10949, 10967, 10971,
  10987, 10995, 11009, 11029, 11043, 11045, 11055, 11063,
  11075, 11081, 11117, 11135, 11141, 11159, 11163, 11181,
  11187, 11225, 11237, 11261, 11279, 11297, 11307, 11309,
  11327, 11329, 11341, 11377, 11403, 11405, 11413, 11427,
  11439, 11453, 11461, 11473, 11479, 11489, 11495, 11499,
  11533, 11545, 11561, 11567, 11575, 11579, 11589, 11611,
  11623, 11637, 11657, 11663, 11687, 11691, 11701, 11747,
  11761, 11773, 11783, 11795, 11797, 11817, 11849, 11855,
  11867, 11869, 11873, 11883, 11919, 11921, 11927, 11933,
  11947, 11955, 11961, 11999, 12027, 12029, 12037, 12041,
  12049, 12055, 12095, 12097, 12107, 12109, 12121, 12127,
  12133, 12137, 12181, 12197, 12207, 12209, 12239, 12253,
  12263, 12269, 12277, 12287, 12295, 12309, 12313, 12335,
  12361, 12367, 12391, 12409, 12415, 12433, 12449, 12469,
  12479, 12481, 12499, 12505, 12517, 12527, 12549, 12559,
  12597, 12615, 12621, 12639, 12643, 12657, 12667, 12707,
  12713, 12727, 12741, 12745, 12763, 12769, 12779, 12781,
  12787, 12799, 12809, 12815, 12829, 12839, 12857, 12875,
  12883, 12889, 12901, 12929, 12947, 12953, 12959, 12969,
  12983, 12987, 12995, 13015, 13019, 13031, 13063, 13077,
  13103, 13137, 13149, 13173, 13207, 13211, 13227, 13241,
  13249, 13255, 13269, 13283, 13285, 13303, 13307, 13321,
  13339, 13351, 13377, 13389, 13407, 13417, 13431, 13435,
  13447, 13459, 13465, 13477, 13501, 13513, 13531, 13543,
  13561, 13581, 13599, 13605, 13617, 13623, 13637, 13647,
  13661, 13677, 13683, 13695, 13725, 13729, 13753, 13773,
  13781, 13785, 13795, 13801, 13807, 13825, 13835, 13855,
  13861, 13871, 13883, 13897, 13905, 13915, 13939, 13941,
  13969, 13979, 13981, 13997, 14027, 14035, 14037, 14051,
  14063, 14085, 14095, 14107, 14113, 14125, 14137, 14145,
  14151, 14163, 14193, 14199, 14219, 14229, 14233, 14243,
  14277, 14287, 14289, 14295, 14301, 14305, 14323, 14339,
  14341, 14359, 14365, 14375, 14387, 14411, 14425, 14441,
  14449, 14499, 14513, 14523, 14537, 14543, 14561, 14579,
  14585, 14593, 14599, 14603, 14611, 14641, 14671, 14695,
  14701, 14723, 14725, 14743, 14753, 14759, 14765, 14795,
  14797, 14803, 14831, 14839, 14845, 14855, 14889, 14895,
  14909, 14929, 14941, 14945, 14951, 14963, 14965, 14985,
  15033, 15039, 15053, 15059, 15061, 15071, 15077, 15081,
  15099, 15121, 15147, 15149, 15157, 15167, 15187, 15193,
  15203, 15205, 15215, 15217, 15223, 15243, 15257, 15269,
  15273, 15287, 15291, 15313, 15335, 15347, 15359, 15373,
  15379, 15381, 15391, 15395, 15397, 15419, 15439, 15453,
  15469, 15491, 15503, 15517, 15527, 15531, 15545, 15559,
  15593, 15611, 15613, 15619, 15639, 15643, 15649, 15661,
  15667, 15669, 15681, 15693, 15717, 15721, 15741, 15745,
  15765, 15793, 15799, 15811, 15825, 15835, 15847, 15851,
  15865, 15877, 15881, 15887, 15899, 15915, 15935, 15937,
  15955, 15973, 15977, 16011, 16035, 16061, 16069, 16087,
  16093, 16097, 16121, 16141, 16153, 16159, 16165, 16183,
  16189, 16195, 16197, 16201, 16209, 16215, 16225, 16259,
  16265, 16273, 16299, 16309, 16355, 16375, 16381
} ;
